TIMEOUT
The TRS could not be proven terminating. The proof attempt took 60022 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (42754ms).
| – Problem 2 was processed with processor DependencyGraph (13026ms).
| | – Problem 74 remains open; application of the following processors failed [].
| | – Problem 75 remains open; application of the following processors failed [].
| – Problem 3 remains open; application of the following processors failed [SubtermCriterion (1ms), DependencyGraph (timeout)].
| – Problem 4 was processed with processor SubtermCriterion (4ms).
| – Problem 5 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 6 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 7 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 8 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 9 was processed with processor SubtermCriterion (2ms).
| | – Problem 69 remains open; application of the following processors failed [].
| – Problem 10 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 11 was processed with processor SubtermCriterion (2ms).
| | – Problem 70 remains open; application of the following processors failed [].
| – Problem 12 remains open; application of the following processors failed [SubtermCriterion (3ms)].
| – Problem 13 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 14 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 15 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 16 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 17 was processed with processor SubtermCriterion (2ms).
| – Problem 18 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 19 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 20 was processed with processor SubtermCriterion (1ms).
| | – Problem 71 remains open; application of the following processors failed [].
| – Problem 21 was processed with processor SubtermCriterion (2ms).
| – Problem 22 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 23 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 24 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 25 was processed with processor SubtermCriterion (2ms).
| | – Problem 72 remains open; application of the following processors failed [].
| – Problem 26 remains open; application of the following processors failed [SubtermCriterion (7ms)].
| – Problem 27 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 28 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 29 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 30 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 31 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 32 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 33 was processed with processor SubtermCriterion (3ms).
| – Problem 34 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 35 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 36 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 37 remains open; application of the following processors failed [SubtermCriterion (3ms)].
| – Problem 38 was processed with processor SubtermCriterion (1ms).
| – Problem 39 was processed with processor SubtermCriterion (2ms).
| – Problem 40 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 41 was processed with processor SubtermCriterion (3ms).
| – Problem 42 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 43 was processed with processor SubtermCriterion (1ms).
| | – Problem 73 remains open; application of the following processors failed [].
| – Problem 44 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 45 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 46 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 47 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 48 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 49 was processed with processor SubtermCriterion (3ms).
| – Problem 50 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 51 was processed with processor SubtermCriterion (1ms).
| – Problem 52 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 53 was processed with processor SubtermCriterion (2ms).
| – Problem 54 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 55 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 56 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 57 was processed with processor SubtermCriterion (3ms).
| – Problem 58 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 59 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 60 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 61 remains open; application of the following processors failed [SubtermCriterion (3ms)].
| – Problem 62 was processed with processor SubtermCriterion (1ms).
| – Problem 63 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 64 was processed with processor SubtermCriterion (1ms).
| – Problem 65 remains open; application of the following processors failed [SubtermCriterion (3ms)].
| – Problem 66 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 67 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 68 remains open; application of the following processors failed [SubtermCriterion (1ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(isList(__(V1, V2))) | → | isList#(V1) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(a) | → | active#(a) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U41(tt, V2)) | → | isNeList#(V2) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| U61#(active(X)) | → | U61#(X) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(U52(tt)) | → | mark#(tt) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U42(tt)) | → | mark#(tt) |
| mark#(isNeList(X)) | → | isNeList#(X) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(isNeList(__(V1, V2))) | → | isNeList#(V1) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(tt) | → | active#(tt) | | mark#(o) | → | active#(o) |
| mark#(U11(X)) | → | mark#(X) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | mark#(u) | → | active#(u) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(U72(tt)) | → | mark#(tt) |
| active#(isList(V)) | → | U11#(isNeList(V)) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isQid(u)) | → | mark#(tt) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 3
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(U51(tt, V2)) | → | U52#(isList(V2)) |
| active#(isQid(a)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | mark#(U61(X)) | → | U61#(mark(X)) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(a) | → | active#(a) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| active#(U21(tt, V2)) | → | U22#(isList(V2)) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | mark#(i) | → | active#(i) |
| mark#(U81(X)) | → | mark#(X) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| active#(isQid(i)) | → | mark#(tt) | | U22#(mark(X)) | → | U22#(X) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | mark#(U31(X)) | → | mark#(X) |
| U61#(active(X)) | → | U61#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| U22#(active(X)) | → | U22#(X) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | U22#(mark(X)) |
| active#(U42(tt)) | → | mark#(tt) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| mark#(U11(X)) | → | U11#(mark(X)) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(tt) | → | active#(tt) | | mark#(o) | → | active#(o) |
| mark#(U11(X)) | → | mark#(X) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | mark#(isList(X)) | → | isList#(X) |
| active#(U11(tt)) | → | mark#(tt) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| mark#(u) | → | active#(u) | | active#(U61(tt)) | → | mark#(tt) |
| active#(isList(nil)) | → | mark#(tt) | | mark#(nil) | → | active#(nil) |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | active#(U72(tt)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(__(nil, X)) | → | mark#(X) |
| active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) | | mark#(U31(X)) | → | active#(U31(mark(X))) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 5
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) | → | U61#(mark(X)) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(a) | → | active#(a) | | mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) |
| active#(U71(tt, P)) | → | U72#(isPal(P)) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | mark#(i) | → | active#(i) |
| mark#(U81(X)) | → | mark#(X) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| active#(isQid(i)) | → | mark#(tt) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | mark#(X) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(isNePal(V)) | → | isQid#(V) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | U61#(active(X)) | → | U61#(X) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U42(tt)) | → | mark#(tt) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(U81(X)) | → | U81#(mark(X)) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | mark#(isList(X)) | → | isList#(X) |
| active#(U11(tt)) | → | mark#(tt) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| mark#(u) | → | active#(u) | | active#(U61(tt)) | → | mark#(tt) |
| active#(isList(nil)) | → | mark#(tt) | | mark#(nil) | → | active#(nil) |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | active#(U72(tt)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | isList#(V2) | | mark#(isList(X)) | → | active#(isList(X)) |
| mark#(U22(X)) | → | mark#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 6
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) | → | U61#(mark(X)) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U72(X)) | → | U72#(mark(X)) | | mark#(a) | → | active#(a) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U21(tt, V2)) | → | U22#(isList(V2)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| mark#(U81(X)) | → | mark#(X) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | active#(U21(tt, V2)) | → | isList#(V2) |
| U61#(active(X)) | → | U61#(X) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | active#(U42(tt)) | → | mark#(tt) |
| mark#(U11(X)) | → | U11#(mark(X)) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(isNeList(__(V1, V2))) | → | isNeList#(V1) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(tt) | → | active#(tt) | | mark#(o) | → | active#(o) |
| mark#(U11(X)) | → | mark#(X) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | U21#(mark(X1), X2) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| active#(U11(tt)) | → | mark#(tt) | | mark#(u) | → | active#(u) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | active#(isList(nil)) | → | mark#(tt) |
| active#(U61(tt)) | → | mark#(tt) | | mark#(nil) | → | active#(nil) |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(U72(tt)) | → | mark#(tt) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 7
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(U61(X)) | → | U61#(mark(X)) |
| mark#(a) | → | active#(a) | | mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) |
| active#(U71(tt, P)) | → | U72#(isPal(P)) | | active#(U21(tt, V2)) | → | U22#(isList(V2)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | U61#(active(X)) | → | U61#(X) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(U52(tt)) | → | mark#(tt) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U42(tt)) | → | mark#(tt) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(U81(X)) | → | U81#(mark(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | mark#(isList(X)) | → | isList#(X) |
| active#(U11(tt)) | → | mark#(tt) | | mark#(u) | → | active#(u) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | active#(U61(tt)) | → | mark#(tt) |
| active#(isList(nil)) | → | mark#(tt) | | mark#(nil) | → | active#(nil) |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(U72(tt)) | → | mark#(tt) | | active#(__(nil, X)) | → | mark#(X) |
| active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) | | mark#(U31(X)) | → | active#(U31(mark(X))) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | isList#(V2) | | mark#(isList(X)) | → | active#(isList(X)) |
| mark#(U22(X)) | → | mark#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 8
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | mark#(U61(X)) | → | U61#(mark(X)) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(a) | → | active#(a) |
| active#(U71(tt, P)) | → | U72#(isPal(P)) | | active#(U21(tt, V2)) | → | U22#(isList(V2)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | mark#(U42(X)) | → | U42#(mark(X)) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| mark#(U71(X1, X2)) | → | U71#(mark(X1), X2) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | U61#(active(X)) | → | U61#(X) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U42(tt)) | → | mark#(tt) | | mark#(U11(X)) | → | U11#(mark(X)) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | active#(isNeList(__(V1, V2))) | → | isNeList#(V1) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | mark#(U42(X)) | → | mark#(X) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| active#(U11(tt)) | → | mark#(tt) | | mark#(u) | → | active#(u) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | active#(U61(tt)) | → | mark#(tt) |
| active#(isList(nil)) | → | mark#(tt) | | mark#(nil) | → | active#(nil) |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | active#(U72(tt)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(__(nil, X)) | → | mark#(X) |
| active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) | | mark#(U31(X)) | → | active#(U31(mark(X))) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 9
Dependency Pairs
| __#(mark(X1), X2) | → | __#(X1, X2) | | __#(active(X1), X2) | → | __#(X1, X2) |
| __#(X1, mark(X2)) | → | __#(X1, X2) | | __#(X1, active(X2)) | → | __#(X1, X2) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 10
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | mark#(U61(X)) | → | U61#(mark(X)) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | mark#(i) | → | active#(i) |
| mark#(U81(X)) | → | mark#(X) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| active#(isQid(i)) | → | mark#(tt) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | mark#(X) |
| mark#(U42(X)) | → | U42#(mark(X)) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| U72#(mark(X)) | → | U72#(X) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| U61#(active(X)) | → | U61#(X) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | active#(U52(tt)) | → | mark#(tt) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U42(tt)) | → | mark#(tt) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(tt) | → | active#(tt) | | mark#(isPal(X)) | → | isPal#(X) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(__(nil, X)) | → | mark#(X) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | mark#(isQid(X)) | → | isQid#(X) |
| active#(isQid(u)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| U72#(active(X)) | → | U72#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 11
Dependency Pairs
| U41#(X1, mark(X2)) | → | U41#(X1, X2) | | U41#(mark(X1), X2) | → | U41#(X1, X2) |
| U41#(X1, active(X2)) | → | U41#(X1, X2) | | U41#(active(X1), X2) | → | U41#(X1, X2) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 12
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | mark#(U42(X)) | → | U42#(mark(X)) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(isNePal(V)) | → | isQid#(V) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U42(tt)) | → | mark#(tt) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| mark#(U11(X)) | → | U11#(mark(X)) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(tt) | → | active#(tt) | | mark#(isPal(X)) | → | isPal#(X) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | mark#(isQid(X)) | → | isQid#(X) |
| active#(isQid(u)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 13
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(U61(X)) | → | U61#(mark(X)) |
| mark#(U72(X)) | → | U72#(mark(X)) | | mark#(a) | → | active#(a) |
| active#(U21(tt, V2)) | → | U22#(isList(V2)) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | mark#(i) | → | active#(i) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | mark#(U81(X)) | → | mark#(X) |
| active#(isQid(i)) | → | mark#(tt) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | mark#(X) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(U21(tt, V2)) | → | isList#(V2) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | U61#(active(X)) | → | U61#(X) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U42(tt)) | → | mark#(tt) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| mark#(U11(X)) | → | U11#(mark(X)) | | active#(isNeList(__(V1, V2))) | → | isNeList#(V1) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | U21#(mark(X1), X2) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(isList(nil)) | → | mark#(tt) | | active#(U61(tt)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(__(nil, X)) | → | mark#(X) | | mark#(U31(X)) | → | active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) | | mark#(isQid(X)) | → | isQid#(X) |
| active#(isQid(u)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 14
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | mark#(U61(X)) | → | U61#(mark(X)) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| active#(U21(tt, V2)) | → | U22#(isList(V2)) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | mark#(i) | → | active#(i) |
| mark#(U81(X)) | → | mark#(X) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| active#(isQid(i)) | → | mark#(tt) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | mark#(X) |
| mark#(U42(X)) | → | U42#(mark(X)) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | mark#(U71(X1, X2)) | → | U71#(mark(X1), X2) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | U72#(mark(X)) | → | U72#(X) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | U61#(active(X)) | → | U61#(X) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U42(tt)) | → | mark#(tt) | | mark#(U11(X)) | → | U11#(mark(X)) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | active#(isNeList(__(V1, V2))) | → | isNeList#(V1) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| active#(U11(tt)) | → | mark#(tt) | | mark#(u) | → | active#(u) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | active#(U61(tt)) | → | mark#(tt) |
| active#(isList(nil)) | → | mark#(tt) | | mark#(nil) | → | active#(nil) |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | active#(U72(tt)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| U72#(active(X)) | → | U72#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 15
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(U61(X)) | → | U61#(mark(X)) |
| mark#(a) | → | active#(a) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | U51#(mark(X1), X2) | → | U51#(X1, X2) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | mark#(U31(X)) | → | mark#(X) |
| U61#(active(X)) | → | U61#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | U22#(mark(X)) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | active#(U42(tt)) | → | mark#(tt) |
| U51#(X1, active(X2)) | → | U51#(X1, X2) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| mark#(U11(X)) | → | U11#(mark(X)) | | active#(isNeList(__(V1, V2))) | → | isNeList#(V1) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| U51#(active(X1), X2) | → | U51#(X1, X2) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(U81(X)) | → | U81#(mark(X)) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | mark#(u) | → | active#(u) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(isNeList(__(V1, V2))) | → | U51#(isNeList(V1), V2) | | active#(U72(tt)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(__(nil, X)) | → | mark#(X) |
| active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) | | mark#(U31(X)) | → | active#(U31(mark(X))) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| mark#(isList(X)) | → | active#(isList(X)) | | U51#(X1, mark(X2)) | → | U51#(X1, X2) |
| mark#(U22(X)) | → | mark#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 16
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(isList(__(V1, V2))) | → | isList#(V1) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(a) | → | active#(a) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U41(tt, V2)) | → | isNeList#(V2) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| U61#(active(X)) | → | U61#(X) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(U52(tt)) | → | mark#(tt) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U42(tt)) | → | mark#(tt) |
| mark#(isNeList(X)) | → | isNeList#(X) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(isNeList(__(V1, V2))) | → | isNeList#(V1) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(tt) | → | active#(tt) | | mark#(o) | → | active#(o) |
| mark#(U11(X)) | → | mark#(X) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(U81(X)) | → | U81#(mark(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| active#(U11(tt)) | → | mark#(tt) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| mark#(u) | → | active#(u) | | active#(U61(tt)) | → | mark#(tt) |
| active#(isList(nil)) | → | mark#(tt) | | mark#(nil) | → | active#(nil) |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(U72(tt)) | → | mark#(tt) | | active#(isList(V)) | → | U11#(isNeList(V)) |
| active#(__(nil, X)) | → | mark#(X) | | mark#(U31(X)) | → | active#(U31(mark(X))) |
| active#(isQid(u)) | → | mark#(tt) | | mark#(isList(X)) | → | active#(isList(X)) |
| mark#(U22(X)) | → | mark#(X) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 19
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | mark#(U61(X)) | → | U61#(mark(X)) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | active#(U21(tt, V2)) | → | U22#(isList(V2)) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | mark#(i) | → | active#(i) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | mark#(U81(X)) | → | mark#(X) |
| active#(isQid(i)) | → | mark#(tt) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | mark#(X) |
| mark#(U42(X)) | → | U42#(mark(X)) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | mark#(U31(X)) | → | mark#(X) |
| U61#(active(X)) | → | U61#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U52(tt)) | → | mark#(tt) |
| active#(U42(tt)) | → | mark#(tt) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| mark#(U11(X)) | → | U11#(mark(X)) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(isPal(X)) | → | isPal#(X) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | U21#(mark(X1), X2) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | active#(isPal(V)) | → | isNePal#(V) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | active#(U72(tt)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| active#(isQid(u)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 18
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(U61(X)) | → | U61#(mark(X)) |
| mark#(a) | → | active#(a) | | mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) |
| active#(U71(tt, P)) | → | U72#(isPal(P)) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | mark#(i) | → | active#(i) |
| mark#(U81(X)) | → | mark#(X) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| active#(isQid(i)) | → | mark#(tt) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | mark#(X) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| U61#(active(X)) | → | U61#(X) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(U52(tt)) | → | mark#(tt) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U42(tt)) | → | mark#(tt) |
| mark#(isNeList(X)) | → | isNeList#(X) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(isNeList(__(V1, V2))) | → | isNeList#(V1) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(tt) | → | active#(tt) | | mark#(o) | → | active#(o) |
| mark#(U11(X)) | → | mark#(X) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(U81(X)) | → | U81#(mark(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| active#(U11(tt)) | → | mark#(tt) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| mark#(u) | → | active#(u) | | active#(U61(tt)) | → | mark#(tt) |
| active#(isList(nil)) | → | mark#(tt) | | mark#(nil) | → | active#(nil) |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | active#(U72(tt)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(__(nil, X)) | → | mark#(X) |
| active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) | | mark#(U31(X)) | → | active#(U31(mark(X))) |
| active#(isQid(u)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 20
Dependency Pairs
| U21#(X1, mark(X2)) | → | U21#(X1, X2) | | U21#(mark(X1), X2) | → | U21#(X1, X2) |
| U21#(active(X1), X2) | → | U21#(X1, X2) | | U21#(X1, active(X2)) | → | U21#(X1, X2) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 23
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(U61(X)) | → | U61#(mark(X)) |
| mark#(a) | → | active#(a) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | mark#(i) | → | active#(i) |
| mark#(U81(X)) | → | mark#(X) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| active#(isQid(i)) | → | mark#(tt) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | mark#(X) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(isNePal(V)) | → | isQid#(V) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | mark#(U31(X)) | → | mark#(X) |
| U61#(active(X)) | → | U61#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | U22#(mark(X)) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | active#(U42(tt)) | → | mark#(tt) |
| mark#(isNeList(X)) | → | isNeList#(X) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(isNeList(__(V1, V2))) | → | isNeList#(V1) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(tt) | → | active#(tt) | | mark#(o) | → | active#(o) |
| mark#(U11(X)) | → | mark#(X) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | mark#(isList(X)) | → | isList#(X) |
| active#(U11(tt)) | → | mark#(tt) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| mark#(u) | → | active#(u) | | active#(U61(tt)) | → | mark#(tt) |
| active#(isList(nil)) | → | mark#(tt) | | mark#(nil) | → | active#(nil) |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(U72(tt)) | → | mark#(tt) | | active#(__(nil, X)) | → | mark#(X) |
| active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) | | mark#(U31(X)) | → | active#(U31(mark(X))) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | isList#(V2) | | mark#(isList(X)) | → | active#(isList(X)) |
| mark#(U22(X)) | → | mark#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 22
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) | → | U61#(mark(X)) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(a) | → | active#(a) | | mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) |
| active#(U71(tt, P)) | → | U72#(isPal(P)) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | mark#(i) | → | active#(i) |
| mark#(U81(X)) | → | mark#(X) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| active#(isQid(i)) | → | mark#(tt) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | mark#(X) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| mark#(U31(X)) | → | mark#(X) | | U61#(active(X)) | → | U61#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | mark#(U22(X)) | → | U22#(mark(X)) |
| active#(U52(tt)) | → | mark#(tt) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U42(tt)) | → | mark#(tt) | | mark#(isNeList(X)) | → | isNeList#(X) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | active#(isNeList(__(V1, V2))) | → | isNeList#(V1) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | mark#(u) | → | active#(u) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(__(nil, X)) | → | mark#(X) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | mark#(isQid(X)) | → | isQid#(X) |
| active#(isQid(u)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 25
Dependency Pairs
| U51#(mark(X1), X2) | → | U51#(X1, X2) | | U51#(X1, mark(X2)) | → | U51#(X1, X2) |
| U51#(X1, active(X2)) | → | U51#(X1, X2) | | U51#(active(X1), X2) | → | U51#(X1, X2) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 24
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(U51(tt, V2)) | → | U52#(isList(V2)) |
| active#(isQid(a)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(a) | → | active#(a) |
| active#(U21(tt, V2)) | → | U22#(isList(V2)) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | mark#(i) | → | active#(i) |
| mark#(U81(X)) | → | mark#(X) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| active#(isQid(i)) | → | mark#(tt) | | U22#(mark(X)) | → | U22#(X) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | mark#(U31(X)) | → | mark#(X) |
| U61#(active(X)) | → | U61#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| U22#(active(X)) | → | U22#(X) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | U22#(mark(X)) |
| active#(U42(tt)) | → | mark#(tt) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| mark#(U11(X)) | → | U11#(mark(X)) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(tt) | → | active#(tt) | | mark#(o) | → | active#(o) |
| mark#(U11(X)) | → | mark#(X) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | mark#(u) | → | active#(u) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(__(nil, X)) | → | mark#(X) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | mark#(isQid(X)) | → | isQid#(X) |
| active#(isQid(u)) | → | mark#(tt) | | mark#(isList(X)) | → | active#(isList(X)) |
| mark#(U22(X)) | → | mark#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 27
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) | → | U61#(mark(X)) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(a) | → | active#(a) | | mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) |
| active#(U71(tt, P)) | → | U72#(isPal(P)) | | active#(U21(tt, V2)) | → | U22#(isList(V2)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| U22#(mark(X)) | → | U22#(X) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | mark#(X) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| U61#(active(X)) | → | U61#(X) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | U22#(active(X)) | → | U22#(X) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | U22#(mark(X)) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U42(tt)) | → | mark#(tt) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | active#(isNeList(__(V1, V2))) | → | isNeList#(V1) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(U72(tt)) | → | mark#(tt) |
| active#(__(nil, X)) | → | mark#(X) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isQid(u)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | isList#(V2) | | mark#(isList(X)) | → | active#(isList(X)) |
| mark#(U22(X)) | → | mark#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 26
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(isList(__(V1, V2))) | → | isList#(V1) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(a) | → | active#(a) |
| active#(U21(tt, V2)) | → | U22#(isList(V2)) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | mark#(i) | → | active#(i) |
| mark#(U81(X)) | → | mark#(X) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| active#(isQid(i)) | → | mark#(tt) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | mark#(X) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(U41(tt, V2)) | → | isNeList#(V2) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | U61#(active(X)) | → | U61#(X) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(U52(tt)) | → | mark#(tt) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U42(tt)) | → | mark#(tt) | | mark#(isNeList(X)) | → | isNeList#(X) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | active#(isNeList(__(V1, V2))) | → | isNeList#(V1) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | mark#(U42(X)) | → | mark#(X) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(U81(X)) | → | U81#(mark(X)) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | mark#(u) | → | active#(u) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(isList(V)) | → | U11#(isNeList(V)) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isQid(u)) | → | mark#(tt) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 29
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(U61(X)) | → | U61#(mark(X)) |
| mark#(U72(X)) | → | U72#(mark(X)) | | mark#(a) | → | active#(a) |
| active#(U71(tt, P)) | → | U72#(isPal(P)) | | mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | U72#(mark(X)) | → | U72#(X) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| mark#(U31(X)) | → | mark#(X) | | U61#(active(X)) | → | U61#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | U22#(mark(X)) |
| active#(U42(tt)) | → | mark#(tt) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| mark#(U11(X)) | → | U11#(mark(X)) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(tt) | → | active#(tt) | | mark#(o) | → | active#(o) |
| mark#(U11(X)) | → | mark#(X) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | mark#(isList(X)) | → | isList#(X) |
| active#(U11(tt)) | → | mark#(tt) | | mark#(u) | → | active#(u) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | active#(U61(tt)) | → | mark#(tt) |
| active#(isList(nil)) | → | mark#(tt) | | mark#(nil) | → | active#(nil) |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | active#(U72(tt)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(__(nil, X)) | → | mark#(X) |
| active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) | | mark#(U31(X)) | → | active#(U31(mark(X))) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | isList#(V2) | | mark#(isList(X)) | → | active#(isList(X)) |
| mark#(U22(X)) | → | mark#(X) | | U72#(active(X)) | → | U72#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 28
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | active#(U21(tt, V2)) | → | U22#(isList(V2)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| mark#(U81(X)) | → | mark#(X) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | mark#(U42(X)) | → | U42#(mark(X)) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| mark#(U31(X)) | → | mark#(X) | | U61#(active(X)) | → | U61#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | active#(U52(tt)) | → | mark#(tt) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U42(tt)) | → | mark#(tt) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | active#(isNeList(__(V1, V2))) | → | isNeList#(V1) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(isPal(X)) | → | isPal#(X) |
| mark#(tt) | → | active#(tt) | | mark#(o) | → | active#(o) |
| mark#(U11(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | U21#(mark(X1), X2) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| active#(U11(tt)) | → | mark#(tt) | | mark#(u) | → | active#(u) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | active#(U61(tt)) | → | mark#(tt) |
| active#(isList(nil)) | → | mark#(tt) | | mark#(nil) | → | active#(nil) |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | active#(U72(tt)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | isList#(V2) | | mark#(isList(X)) | → | active#(isList(X)) |
| mark#(U22(X)) | → | mark#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 31
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | mark#(U61(X)) | → | U61#(mark(X)) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(a) | → | active#(a) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | mark#(i) | → | active#(i) |
| mark#(U81(X)) | → | mark#(X) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| active#(isQid(i)) | → | mark#(tt) | | active#(isPal(V)) | → | U81#(isNePal(V)) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | mark#(U42(X)) | → | U42#(mark(X)) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(isNePal(V)) | → | isQid#(V) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | U61#(active(X)) | → | U61#(X) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U52(tt)) | → | mark#(tt) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U42(tt)) | → | mark#(tt) | | mark#(U11(X)) | → | U11#(mark(X)) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(isPal(X)) | → | isPal#(X) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | U21#(mark(X1), X2) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | mark#(isList(X)) | → | isList#(X) |
| active#(U11(tt)) | → | mark#(tt) | | mark#(u) | → | active#(u) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | active#(isList(nil)) | → | mark#(tt) |
| active#(U61(tt)) | → | mark#(tt) | | mark#(nil) | → | active#(nil) |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | active#(U72(tt)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(__(nil, X)) | → | mark#(X) |
| active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) | | mark#(U31(X)) | → | active#(U31(mark(X))) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| mark#(isList(X)) | → | active#(isList(X)) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(U22(X)) | → | mark#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 30
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) | → | U61#(mark(X)) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U72(X)) | → | U72#(mark(X)) | | mark#(a) | → | active#(a) |
| active#(U71(tt, P)) | → | U72#(isPal(P)) | | mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(isNePal(V)) | → | isQid#(V) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| U72#(mark(X)) | → | U72#(X) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(U52(tt)) | → | mark#(tt) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U42(tt)) | → | mark#(tt) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | mark#(u) | → | active#(u) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | mark#(isQid(X)) | → | isQid#(X) |
| active#(isQid(u)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| U72#(active(X)) | → | U72#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 34
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | active#(U21(tt, V2)) | → | U22#(isList(V2)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | mark#(U42(X)) | → | U42#(mark(X)) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| mark#(U71(X1, X2)) | → | U71#(mark(X1), X2) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | U61#(active(X)) | → | U61#(X) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U42(tt)) | → | mark#(tt) | | mark#(U11(X)) | → | U11#(mark(X)) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | active#(isNeList(__(V1, V2))) | → | isNeList#(V1) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(isPal(X)) | → | isPal#(X) |
| mark#(tt) | → | active#(tt) | | mark#(o) | → | active#(o) |
| mark#(U11(X)) | → | mark#(X) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(__(nil, X)) | → | mark#(X) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | mark#(isQid(X)) | → | isQid#(X) |
| active#(isQid(u)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 35
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(isQid(a)) | → | mark#(tt) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(a) | → | active#(a) |
| active#(U21(tt, V2)) | → | U22#(isList(V2)) | | mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) |
| active#(U71(tt, P)) | → | U72#(isPal(P)) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | mark#(i) | → | active#(i) |
| mark#(U81(X)) | → | mark#(X) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| active#(isQid(i)) | → | mark#(tt) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | mark#(X) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(U52(X)) | → | mark#(X) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U42(tt)) | → | mark#(tt) | | mark#(isNeList(X)) | → | isNeList#(X) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | active#(isNeList(__(V1, V2))) | → | isNeList#(V1) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(U81(X)) | → | U81#(mark(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | mark#(u) | → | active#(u) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| active#(isQid(u)) | → | mark#(tt) | | mark#(isList(X)) | → | active#(isList(X)) |
| mark#(U22(X)) | → | mark#(X) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 32
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(U61(X)) | → | U61#(mark(X)) |
| mark#(U72(X)) | → | U72#(mark(X)) | | mark#(a) | → | active#(a) |
| active#(U71(tt, P)) | → | U72#(isPal(P)) | | mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(isNePal(V)) | → | isQid#(V) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | U72#(mark(X)) | → | U72#(X) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U42(tt)) | → | mark#(tt) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | mark#(u) | → | active#(u) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | active#(__(nil, X)) | → | mark#(X) |
| active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) | | mark#(U31(X)) | → | active#(U31(mark(X))) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | isList#(V2) | | mark#(isList(X)) | → | active#(isList(X)) |
| mark#(U22(X)) | → | mark#(X) | | U72#(active(X)) | → | U72#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 36
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | mark#(U42(X)) | → | U42#(mark(X)) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| U61#(active(X)) | → | U61#(X) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(U52(tt)) | → | mark#(tt) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U42(tt)) | → | mark#(tt) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | mark#(U11(X)) | → | U11#(mark(X)) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(isPal(X)) | → | isPal#(X) |
| mark#(tt) | → | active#(tt) | | mark#(o) | → | active#(o) |
| mark#(U11(X)) | → | mark#(X) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(U72(tt)) | → | mark#(tt) |
| active#(__(nil, X)) | → | mark#(X) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | mark#(isQid(X)) | → | isQid#(X) |
| active#(isQid(u)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 37
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | mark#(U42(X)) | → | U42#(mark(X)) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| mark#(U71(X1, X2)) | → | U71#(mark(X1), X2) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| U72#(mark(X)) | → | U72#(X) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| U61#(active(X)) | → | U61#(X) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | active#(U52(tt)) | → | mark#(tt) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U42(tt)) | → | mark#(tt) |
| mark#(U11(X)) | → | U11#(mark(X)) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(isPal(X)) | → | isPal#(X) | | mark#(o) | → | active#(o) |
| mark#(U11(X)) | → | mark#(X) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | mark#(u) | → | active#(u) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(__(nil, X)) | → | mark#(X) | | mark#(isNePal(X)) | → | isNePal#(X) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | isList#(V2) | | mark#(isList(X)) | → | active#(isList(X)) |
| mark#(U22(X)) | → | mark#(X) | | U72#(active(X)) | → | U72#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 42
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | mark#(U42(X)) | → | U42#(mark(X)) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| U61#(active(X)) | → | U61#(X) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(U52(tt)) | → | mark#(tt) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U42(tt)) | → | mark#(tt) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | mark#(U11(X)) | → | U11#(mark(X)) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(isPal(X)) | → | isPal#(X) | | mark#(o) | → | active#(o) |
| mark#(U11(X)) | → | mark#(X) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | mark#(isList(X)) | → | isList#(X) |
| active#(U11(tt)) | → | mark#(tt) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| mark#(u) | → | active#(u) | | active#(U61(tt)) | → | mark#(tt) |
| active#(isList(nil)) | → | mark#(tt) | | mark#(nil) | → | active#(nil) |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | active#(U72(tt)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(__(nil, X)) | → | mark#(X) |
| active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) | | mark#(U31(X)) | → | active#(U31(mark(X))) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | isList#(V2) | | mark#(isList(X)) | → | active#(isList(X)) |
| mark#(U22(X)) | → | mark#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 43
Dependency Pairs
| U71#(X1, active(X2)) | → | U71#(X1, X2) | | U71#(active(X1), X2) | → | U71#(X1, X2) |
| U71#(mark(X1), X2) | → | U71#(X1, X2) | | U71#(X1, mark(X2)) | → | U71#(X1, X2) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 40
Dependency Pairs
| U72#(mark(X)) | → | U72#(X) | | mark#(U72(X)) | → | U72#(mark(X)) |
| U72#(active(X)) | → | U72#(X) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 46
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) | → | U61#(mark(X)) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U72(X)) | → | U72#(mark(X)) | | mark#(a) | → | active#(a) |
| active#(U71(tt, P)) | → | U72#(isPal(P)) | | mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | U72#(mark(X)) | → | U72#(X) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| U61#(active(X)) | → | U61#(X) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | U22#(mark(X)) |
| active#(U42(tt)) | → | mark#(tt) | | mark#(isNeList(X)) | → | isNeList#(X) |
| mark#(U11(X)) | → | U11#(mark(X)) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(isNeList(__(V1, V2))) | → | isNeList#(V1) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(tt) | → | active#(tt) | | mark#(o) | → | active#(o) |
| mark#(U11(X)) | → | mark#(X) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(U81(X)) | → | U81#(mark(X)) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | mark#(u) | → | active#(u) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(U72(tt)) | → | mark#(tt) |
| active#(__(nil, X)) | → | mark#(X) | | mark#(U31(X)) | → | active#(U31(mark(X))) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| U72#(active(X)) | → | U72#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 47
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | mark#(U61(X)) | → | U61#(mark(X)) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(a) | → | active#(a) |
| active#(U71(tt, P)) | → | U72#(isPal(P)) | | active#(U21(tt, V2)) | → | U22#(isList(V2)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | mark#(U42(X)) | → | U42#(mark(X)) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| U61#(active(X)) | → | U61#(X) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | active#(U52(tt)) | → | mark#(tt) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U42(tt)) | → | mark#(tt) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | active#(isNeList(__(V1, V2))) | → | isNeList#(V1) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(U81(X)) | → | U81#(mark(X)) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(__(nil, X)) | → | mark#(X) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | mark#(isQid(X)) | → | isQid#(X) |
| active#(isQid(u)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 44
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(U61(X)) | → | U61#(mark(X)) |
| mark#(U72(X)) | → | U72#(mark(X)) | | mark#(a) | → | active#(a) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| U72#(mark(X)) | → | U72#(X) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| U61#(active(X)) | → | U61#(X) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | active#(U52(tt)) | → | mark#(tt) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U42(tt)) | → | mark#(tt) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | mark#(U11(X)) | → | U11#(mark(X)) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | mark#(u) | → | active#(u) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(U72(tt)) | → | mark#(tt) |
| active#(__(nil, X)) | → | mark#(X) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isQid(u)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | isList#(V2) | | mark#(isList(X)) | → | active#(isList(X)) |
| mark#(U22(X)) | → | mark#(X) | | U72#(active(X)) | → | U72#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 45
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(U61(X)) | → | U61#(mark(X)) |
| mark#(U72(X)) | → | U72#(mark(X)) | | mark#(a) | → | active#(a) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | U72#(mark(X)) | → | U72#(X) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(U21(tt, V2)) | → | isList#(V2) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | U61#(active(X)) | → | U61#(X) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(U52(tt)) | → | mark#(tt) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U42(tt)) | → | mark#(tt) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(U72(tt)) | → | mark#(tt) |
| active#(__(nil, X)) | → | mark#(X) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | mark#(isQid(X)) | → | isQid#(X) |
| active#(isQid(u)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| U72#(active(X)) | → | U72#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 50
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(U61(X)) | → | U61#(mark(X)) |
| mark#(U72(X)) | → | U72#(mark(X)) | | mark#(a) | → | active#(a) |
| active#(U71(tt, P)) | → | U72#(isPal(P)) | | mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | U72#(mark(X)) | → | U72#(X) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(U21(tt, V2)) | → | isList#(V2) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | mark#(U31(X)) | → | mark#(X) |
| U61#(active(X)) | → | U61#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U52(tt)) | → | mark#(tt) |
| mark#(U22(X)) | → | U22#(mark(X)) | | active#(U42(tt)) | → | mark#(tt) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | mark#(U11(X)) | → | U11#(mark(X)) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(__(nil, X)) | → | mark#(X) | | mark#(U31(X)) | → | active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) | | mark#(isQid(X)) | → | isQid#(X) |
| active#(isQid(u)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| U72#(active(X)) | → | U72#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 48
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(U61(X)) | → | U61#(mark(X)) |
| mark#(U72(X)) | → | U72#(mark(X)) | | mark#(a) | → | active#(a) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U21(tt, V2)) | → | U22#(isList(V2)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| mark#(U81(X)) | → | mark#(X) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | U61#(active(X)) | → | U61#(X) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U42(tt)) | → | mark#(tt) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| mark#(U11(X)) | → | U11#(mark(X)) | | active#(isNeList(__(V1, V2))) | → | isNeList#(V1) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | U21#(mark(X1), X2) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | mark#(isList(X)) | → | isList#(X) |
| active#(U11(tt)) | → | mark#(tt) | | mark#(u) | → | active#(u) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | active#(isList(nil)) | → | mark#(tt) |
| active#(U61(tt)) | → | mark#(tt) | | mark#(nil) | → | active#(nil) |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | active#(U72(tt)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | isList#(V2) | | mark#(isList(X)) | → | active#(isList(X)) |
| mark#(U22(X)) | → | mark#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 55
Dependency Pairs
| U81#(mark(X)) | → | U81#(X) | | active#(isPal(V)) | → | U81#(isNePal(V)) |
| U81#(active(X)) | → | U81#(X) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 54
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | mark#(U61(X)) | → | U61#(mark(X)) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(a) | → | active#(a) |
| active#(U71(tt, P)) | → | U72#(isPal(P)) | | active#(U21(tt, V2)) | → | U22#(isList(V2)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | mark#(U42(X)) | → | U42#(mark(X)) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| mark#(U71(X1, X2)) | → | U71#(mark(X1), X2) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | U61#(active(X)) | → | U61#(X) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U42(tt)) | → | mark#(tt) | | mark#(U11(X)) | → | U11#(mark(X)) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | active#(isNeList(__(V1, V2))) | → | isNeList#(V1) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(U81(X)) | → | U81#(mark(X)) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(U72(tt)) | → | mark#(tt) |
| active#(__(nil, X)) | → | mark#(X) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | mark#(isQid(X)) | → | isQid#(X) |
| active#(isQid(u)) | → | mark#(tt) | | mark#(isList(X)) | → | active#(isList(X)) |
| mark#(U22(X)) | → | mark#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 52
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(U51(tt, V2)) | → | U52#(isList(V2)) |
| active#(isQid(a)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U42(X)) | → | U42#(mark(X)) | | mark#(U72(X)) | → | mark#(X) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| U72#(mark(X)) | → | U72#(X) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(U21(tt, V2)) | → | isList#(V2) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| mark#(U31(X)) | → | mark#(X) | | U61#(active(X)) | → | U61#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U52(tt)) | → | mark#(tt) | | active#(U42(tt)) | → | mark#(tt) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | mark#(U11(X)) | → | U11#(mark(X)) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(__(nil, X)) | → | mark#(X) | | mark#(U31(X)) | → | active#(U31(mark(X))) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| U72#(active(X)) | → | U72#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 59
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| active#(isList(__(V1, V2))) | → | isList#(V1) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | mark#(i) | → | active#(i) |
| mark#(U81(X)) | → | mark#(X) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| active#(isQid(i)) | → | mark#(tt) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | mark#(X) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(U81(tt)) | → | mark#(tt) | | active#(isNeList(V)) | → | U31#(isQid(V)) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | U72#(mark(X)) | → | U72#(X) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | active#(U42(tt)) | → | mark#(tt) |
| mark#(isNeList(X)) | → | isNeList#(X) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | mark#(u) | → | active#(u) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | active#(__(nil, X)) | → | mark#(X) |
| active#(__(__(X, Y), Z)) | → | __#(Y, Z) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | mark#(isQid(X)) | → | isQid#(X) |
| active#(isQid(u)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| U72#(active(X)) | → | U72#(X) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 58
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | active#(U21(tt, V2)) | → | U22#(isList(V2)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | mark#(U42(X)) | → | U42#(mark(X)) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| mark#(U71(X1, X2)) | → | U71#(mark(X1), X2) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | U61#(active(X)) | → | U61#(X) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U42(tt)) | → | mark#(tt) | | mark#(U11(X)) | → | U11#(mark(X)) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | active#(isNeList(__(V1, V2))) | → | isNeList#(V1) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| active#(U11(tt)) | → | mark#(tt) | | mark#(u) | → | active#(u) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | active#(U61(tt)) | → | mark#(tt) |
| active#(isList(nil)) | → | mark#(tt) | | mark#(nil) | → | active#(nil) |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | active#(U72(tt)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | isList#(V2) | | mark#(isList(X)) | → | active#(isList(X)) |
| mark#(U22(X)) | → | mark#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 56
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) | → | U61#(mark(X)) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(a) | → | active#(a) | | mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) |
| active#(U71(tt, P)) | → | U72#(isPal(P)) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | mark#(i) | → | active#(i) |
| mark#(U81(X)) | → | mark#(X) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| active#(isQid(i)) | → | mark#(tt) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | mark#(X) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(isNePal(V)) | → | isQid#(V) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | U61#(active(X)) | → | U61#(X) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U42(tt)) | → | mark#(tt) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(isNeList(__(V1, V2))) | → | isNeList#(V1) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(tt) | → | active#(tt) | | mark#(o) | → | active#(o) |
| mark#(U11(X)) | → | mark#(X) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(U81(X)) | → | U81#(mark(X)) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | mark#(u) | → | active#(u) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(__(nil, X)) | → | mark#(X) | | mark#(U31(X)) | → | active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) | | mark#(isQid(X)) | → | isQid#(X) |
| active#(isQid(u)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 63
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(a) | → | active#(a) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(isNeList(V)) | → | U31#(isQid(V)) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| active#(U21(tt, V2)) | → | isList#(V2) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U52(tt)) | → | mark#(tt) | | active#(U42(tt)) | → | mark#(tt) |
| active#(isList(__(V1, V2))) | → | U21#(isList(V1), V2) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(isNeList(__(V1, V2))) | → | isNeList#(V1) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(tt) | → | active#(tt) | | mark#(isPal(X)) | → | isPal#(X) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | active#(isPal(V)) | → | isNePal#(V) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | active#(U72(tt)) | → | mark#(tt) |
| active#(__(nil, X)) | → | mark#(X) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isQid(u)) | → | mark#(tt) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 61
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | mark#(U61(X)) | → | U61#(mark(X)) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | mark#(i) | → | active#(i) |
| mark#(U81(X)) | → | mark#(X) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| active#(isQid(i)) | → | mark#(tt) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | mark#(X) |
| mark#(U42(X)) | → | U42#(mark(X)) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U81(tt)) | → | mark#(tt) |
| mark#(isPal(X)) | → | active#(isPal(X)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U52(X)) | → | mark#(X) |
| mark#(U71(X1, X2)) | → | mark#(X1) | | mark#(isQid(X)) | → | active#(isQid(X)) |
| active#(U31(tt)) | → | mark#(tt) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| U72#(mark(X)) | → | U72#(X) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| U61#(active(X)) | → | U61#(X) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | active#(U52(tt)) | → | mark#(tt) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U42(tt)) | → | mark#(tt) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(tt) | → | active#(tt) | | mark#(isPal(X)) | → | isPal#(X) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | active#(isPal(V)) | → | isNePal#(V) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U61(X)) | → | mark#(X) |
| active#(isQid(o)) | → | mark#(tt) | | active#(U72(tt)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(isQid(X)) | → | isQid#(X) | | active#(isQid(u)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | isList#(V2) | | mark#(isList(X)) | → | active#(isList(X)) |
| mark#(U22(X)) | → | mark#(X) | | U72#(active(X)) | → | U72#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 60
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(isList(__(V1, V2))) | → | isList#(V1) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(a) | → | active#(a) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U41(tt, V2)) | → | isNeList#(V2) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| U61#(active(X)) | → | U61#(X) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(U52(tt)) | → | mark#(tt) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U42(tt)) | → | mark#(tt) |
| mark#(isNeList(X)) | → | isNeList#(X) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(U81(X)) | → | U81#(mark(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | mark#(u) | → | active#(u) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| U61#(mark(X)) | → | U61#(X) | | active#(U72(tt)) | → | mark#(tt) |
| active#(isList(V)) | → | U11#(isNeList(V)) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isQid(u)) | → | mark#(tt) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 68
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | mark#(U61(X)) | → | U61#(mark(X)) |
| active#(__(X, nil)) | → | mark#(X) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | active#(U21(tt, V2)) | → | U22#(isList(V2)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U72(X)) | → | mark#(X) | | mark#(U42(X)) | → | U42#(mark(X)) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| mark#(U31(X)) | → | mark#(X) | | U61#(active(X)) | → | U61#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(isList(V)) | → | mark#(U11(isNeList(V))) | | active#(U52(tt)) | → | mark#(tt) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U42(tt)) | → | mark#(tt) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | active#(isNeList(__(V1, V2))) | → | isNeList#(V1) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | U21#(mark(X1), X2) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(U52(X)) | → | active#(U52(mark(X))) | | mark#(u) | → | active#(u) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(__(nil, X)) | → | mark#(X) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | mark#(isQid(X)) | → | isQid#(X) |
| active#(isQid(u)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 65
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(isList(__(V1, V2))) | → | isList#(V1) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | active#(U21(tt, V2)) | → | U22#(isList(V2)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U42(X)) | → | U42#(mark(X)) | | mark#(U72(X)) | → | mark#(X) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(U52(X)) | → | mark#(X) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| U61#(active(X)) | → | U61#(X) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(U52(tt)) | → | mark#(tt) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U42(tt)) | → | mark#(tt) |
| mark#(isNeList(X)) | → | isNeList#(X) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(U81(X)) | → | U81#(mark(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(isList(V)) | → | U11#(isNeList(V)) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isQid(u)) | → | mark#(tt) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 66
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| active#(U21(tt, V2)) | → | U22#(isList(V2)) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| mark#(e) | → | active#(e) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| active#(U22(tt)) | → | mark#(tt) | | mark#(i) | → | active#(i) |
| mark#(U81(X)) | → | mark#(X) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| active#(isQid(i)) | → | mark#(tt) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | mark#(X) |
| mark#(U42(X)) | → | U42#(mark(X)) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | mark#(U71(X1, X2)) | → | U71#(mark(X1), X2) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | U72#(mark(X)) | → | U72#(X) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | U61#(active(X)) | → | U61#(X) |
| mark#(U31(X)) | → | mark#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| active#(U52(tt)) | → | mark#(tt) | | mark#(U22(X)) | → | active#(U22(mark(X))) |
| active#(U42(tt)) | → | mark#(tt) | | mark#(U11(X)) | → | U11#(mark(X)) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(tt) | → | active#(tt) | | mark#(o) | → | active#(o) |
| mark#(U11(X)) | → | mark#(X) | | mark#(U42(X)) | → | mark#(X) |
| mark#(U21(X1, X2)) | → | mark#(X1) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(__(nil, X)) | → | mark#(X) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | mark#(isQid(X)) | → | isQid#(X) |
| active#(isQid(u)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| U72#(active(X)) | → | U72#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Open Dependency Pair Problem 67
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(U51(tt, V2)) | → | U52#(isList(V2)) |
| active#(isQid(a)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | mark#(U81(X)) | → | mark#(X) |
| active#(U71(tt, P)) | → | mark#(U72(isPal(P))) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(U72(X)) | → | active#(U72(mark(X))) | | mark#(__(X1, X2)) | → | mark#(X2) |
| mark#(U42(X)) | → | U42#(mark(X)) | | mark#(U72(X)) | → | mark#(X) |
| active#(isQid(e)) | → | mark#(tt) | | mark#(U81(X)) | → | active#(U81(mark(X))) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| U72#(mark(X)) | → | U72#(X) | | mark#(U42(X)) | → | active#(U42(mark(X))) |
| mark#(isNeList(X)) | → | active#(isNeList(X)) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(isNePal(V)) | → | mark#(U61(isQid(V))) | | mark#(U31(X)) | → | mark#(X) |
| U61#(active(X)) | → | U61#(X) | | active#(isPal(nil)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X1) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U52(tt)) | → | mark#(tt) |
| active#(U42(tt)) | → | mark#(tt) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| mark#(U11(X)) | → | U11#(mark(X)) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(tt) | → | active#(tt) | | mark#(isPal(X)) | → | isPal#(X) |
| mark#(o) | → | active#(o) | | mark#(U11(X)) | → | mark#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(U61(tt)) | → | mark#(tt) | | active#(isList(nil)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| mark#(U61(X)) | → | active#(U61(mark(X))) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U11(X)) | → | active#(U11(mark(X))) | | mark#(U41(X1, X2)) | → | mark#(X1) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(__(nil, X)) | → | mark#(X) | | active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | mark#(isQid(X)) | → | isQid#(X) |
| active#(isQid(u)) | → | mark#(tt) | | active#(U51(tt, V2)) | → | isList#(V2) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| U72#(active(X)) | → | U72#(X) | | active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, U31, isQid, nil
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| active#(U71(tt, P)) | → | isPal#(P) | | active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) |
| active#(U51(tt, V2)) | → | U52#(isList(V2)) | | active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) |
| active#(isList(__(V1, V2))) | → | isList#(V1) | | mark#(U61(X)) | → | U61#(mark(X)) |
| active#(__(__(X, Y), Z)) | → | __#(X, __(Y, Z)) | | mark#(U72(X)) | → | U72#(mark(X)) |
| mark#(a) | → | active#(a) | | mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) |
| U71#(X1, mark(X2)) | → | U71#(X1, X2) | | active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) |
| U81#(active(X)) | → | U81#(X) | | mark#(e) | → | active#(e) |
| U51#(mark(X1), X2) | → | U51#(X1, X2) | | __#(active(X1), X2) | → | __#(X1, X2) |
| active#(U22(tt)) | → | mark#(tt) | | active#(isQid(i)) | → | mark#(tt) |
| U21#(X1, active(X2)) | → | U21#(X1, X2) | | active#(isPal(V)) | → | U81#(isNePal(V)) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(U72(X)) | → | mark#(X) | | mark#(U42(X)) | → | U42#(mark(X)) |
| active#(U41(tt, V2)) | → | U42#(isNeList(V2)) | | __#(mark(X1), X2) | → | __#(X1, X2) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | mark#(U71(X1, X2)) | → | U71#(mark(X1), X2) |
| active#(U41(tt, V2)) | → | isNeList#(V2) | | U81#(mark(X)) | → | U81#(X) |
| active#(isNeList(V)) | → | U31#(isQid(V)) | | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) |
| mark#(U52(X)) | → | mark#(X) | | U41#(active(X1), X2) | → | U41#(X1, X2) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| mark#(U31(X)) | → | mark#(X) | | U61#(active(X)) | → | U61#(X) |
| mark#(__(X1, X2)) | → | mark#(X1) | | mark#(U22(X)) | → | U22#(mark(X)) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U42(tt)) | → | mark#(tt) |
| active#(isList(__(V1, V2))) | → | U21#(isList(V1), V2) | | U51#(X1, active(X2)) | → | U51#(X1, X2) |
| active#(isNeList(__(V1, V2))) | → | isNeList#(V1) | | mark#(tt) | → | active#(tt) |
| mark#(o) | → | active#(o) | | active#(isNeList(__(V1, V2))) | → | isList#(V1) |
| mark#(U11(X)) | → | mark#(X) | | active#(isNeList(V)) | → | mark#(U31(isQid(V))) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| U21#(X1, mark(X2)) | → | U21#(X1, X2) | | mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) |
| active#(isPal(V)) | → | isNePal#(V) | | U71#(mark(X1), X2) | → | U71#(X1, X2) |
| U41#(X1, active(X2)) | → | U41#(X1, X2) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U61(X)) | → | mark#(X) |
| U11#(mark(X)) | → | U11#(X) | | active#(isNeList(__(V1, V2))) | → | U51#(isNeList(V1), V2) |
| active#(isQid(o)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(U72(tt)) | → | mark#(tt) | | U21#(active(X1), X2) | → | U21#(X1, X2) |
| __#(X1, mark(X2)) | → | __#(X1, X2) | | active#(__(__(X, Y), Z)) | → | __#(Y, Z) |
| isQid#(mark(X)) | → | isQid#(X) | | mark#(isQid(X)) | → | isQid#(X) |
| U51#(X1, mark(X2)) | → | U51#(X1, X2) | | mark#(U22(X)) | → | mark#(X) |
| mark#(U31(X)) | → | U31#(mark(X)) | | active#(isNePal(__(I, __(P, I)))) | → | U71#(isQid(I), P) |
| active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) | | mark#(__(X1, X2)) | → | __#(mark(X1), mark(X2)) |
| U11#(active(X)) | → | U11#(X) | | active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) |
| active#(isQid(a)) | → | mark#(tt) | | active#(__(X, nil)) | → | mark#(X) |
| active#(U21(tt, V2)) | → | U22#(isList(V2)) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| isList#(active(X)) | → | isList#(X) | | U42#(active(X)) | → | U42#(X) |
| __#(X1, active(X2)) | → | __#(X1, X2) | | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) |
| U42#(mark(X)) | → | U42#(X) | | mark#(U52(X)) | → | U52#(mark(X)) |
| mark#(i) | → | active#(i) | | isNeList#(active(X)) | → | isNeList#(X) |
| mark#(U81(X)) | → | mark#(X) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| U52#(active(X)) | → | U52#(X) | | U22#(mark(X)) | → | U22#(X) |
| isPal#(active(X)) | → | isPal#(X) | | active#(isQid(e)) | → | mark#(tt) |
| active#(isNePal(V)) | → | isQid#(V) | | U41#(X1, mark(X2)) | → | U41#(X1, X2) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(U41(X1, X2)) | → | U41#(mark(X1), X2) | | U71#(X1, active(X2)) | → | U71#(X1, X2) |
| U72#(mark(X)) | → | U72#(X) | | active#(isNePal(V)) | → | U61#(isQid(V)) |
| active#(U21(tt, V2)) | → | isList#(V2) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| active#(isPal(nil)) | → | mark#(tt) | | U22#(active(X)) | → | U22#(X) |
| active#(U52(tt)) | → | mark#(tt) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| U31#(mark(X)) | → | U31#(X) | | mark#(isNeList(X)) | → | isNeList#(X) |
| isNeList#(mark(X)) | → | isNeList#(X) | | mark#(U11(X)) | → | U11#(mark(X)) |
| active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(isPal(X)) | → | isPal#(X) | | isPal#(mark(X)) | → | isPal#(X) |
| mark#(U42(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| mark#(U21(X1, X2)) | → | U21#(mark(X1), X2) | | U51#(active(X1), X2) | → | U51#(X1, X2) |
| active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) | | mark#(U81(X)) | → | U81#(mark(X)) |
| mark#(isNePal(X)) | → | active#(isNePal(X)) | | mark#(U51(X1, X2)) | → | mark#(X1) |
| mark#(isList(X)) | → | isList#(X) | | isList#(mark(X)) | → | isList#(X) |
| active#(U11(tt)) | → | mark#(tt) | | active#(U61(tt)) | → | mark#(tt) |
| active#(isList(nil)) | → | mark#(tt) | | active#(isNeList(V)) | → | isQid#(V) |
| mark#(nil) | → | active#(nil) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | | U41#(mark(X1), X2) | → | U41#(X1, X2) |
| active#(isNeList(__(V1, V2))) | → | U41#(isList(V1), V2) | | isQid#(active(X)) | → | isQid#(X) |
| U31#(active(X)) | → | U31#(X) | | isNePal#(active(X)) | → | isNePal#(X) |
| active#(isList(V)) | → | U11#(isNeList(V)) | | active#(__(nil, X)) | → | mark#(X) |
| active#(isList(V)) | → | isNeList#(V) | | mark#(U31(X)) | → | active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) | → | isQid#(I) | | mark#(isNePal(X)) | → | isNePal#(X) |
| isNePal#(mark(X)) | → | isNePal#(X) | | active#(isQid(u)) | → | mark#(tt) |
| mark#(isList(X)) | → | active#(isList(X)) | | active#(U51(tt, V2)) | → | isList#(V2) |
| U21#(mark(X1), X2) | → | U21#(X1, X2) | | U71#(active(X1), X2) | → | U71#(X1, X2) |
| U52#(mark(X)) | → | U52#(X) | | U72#(active(X)) | → | U72#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
The following SCCs where found
| U41#(X1, mark(X2)) → U41#(X1, X2) | U41#(X1, active(X2)) → U41#(X1, X2) |
| U41#(mark(X1), X2) → U41#(X1, X2) | U41#(active(X1), X2) → U41#(X1, X2) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | mark#(U61(X)) → U61#(mark(X)) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| mark#(U72(X)) → U72#(mark(X)) | active#(U21(tt, V2)) → U22#(isList(V2)) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U42(X)) → U42#(mark(X)) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| mark#(U71(X1, X2)) → U71#(mark(X1), X2) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | mark#(U31(X)) → mark#(X) |
| U61#(active(X)) → U61#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U52(tt)) → mark#(tt) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| mark#(U11(X)) → U11#(mark(X)) | active#(isNeList(__(V1, V2))) → isNeList#(V1) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| active#(U11(tt)) → mark#(tt) | mark#(U52(X)) → active#(U52(mark(X))) |
| mark#(u) → active#(u) | active#(isList(nil)) → mark#(tt) |
| active#(U61(tt)) → mark#(tt) | mark#(nil) → active#(nil) |
| mark#(U61(X)) → active#(U61(mark(X))) | mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(U31(X)) → active#(U31(mark(X))) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | active#(U51(tt, V2)) → isList#(V2) |
| mark#(U22(X)) → mark#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| isNeList#(active(X)) → isNeList#(X) | isNeList#(mark(X)) → isNeList#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) → U61#(mark(X)) | active#(__(X, nil)) → mark#(X) |
| mark#(a) → active#(a) | mark#(U72(X)) → U72#(mark(X)) |
| mark#(U51(X1, X2)) → U51#(mark(X1), X2) | active#(U71(tt, P)) → U72#(isPal(P)) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| U72#(mark(X)) → U72#(X) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| U61#(active(X)) → U61#(X) | mark#(U31(X)) → mark#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| mark#(U22(X)) → U22#(mark(X)) | active#(U52(tt)) → mark#(tt) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | mark#(U11(X)) → U11#(mark(X)) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(tt) → active#(tt) | mark#(o) → active#(o) |
| mark#(U11(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| mark#(U42(X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) → active#(isNePal(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) → mark#(X1) | mark#(isList(X)) → isList#(X) |
| active#(U11(tt)) → mark#(tt) | mark#(U52(X)) → active#(U52(mark(X))) |
| mark#(u) → active#(u) | active#(isList(nil)) → mark#(tt) |
| active#(U61(tt)) → mark#(tt) | mark#(nil) → active#(nil) |
| mark#(U61(X)) → active#(U61(mark(X))) | mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| mark#(U31(X)) → active#(U31(mark(X))) | active#(isNePal(__(I, __(P, I)))) → isQid#(I) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | active#(U51(tt, V2)) → isList#(V2) |
| mark#(U22(X)) → mark#(X) | U72#(active(X)) → U72#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) → mark#(X) | mark#(U61(X)) → U61#(mark(X)) |
| mark#(a) → active#(a) | mark#(U72(X)) → U72#(mark(X)) |
| mark#(U51(X1, X2)) → U51#(mark(X1), X2) | active#(U71(tt, P)) → U72#(isPal(P)) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| U72#(mark(X)) → U72#(X) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | U61#(active(X)) → U61#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| mark#(U22(X)) → U22#(mark(X)) | active#(U52(tt)) → mark#(tt) |
| active#(isList(V)) → mark#(U11(isNeList(V))) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U42(tt)) → mark#(tt) | mark#(isNeList(X)) → isNeList#(X) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | mark#(U11(X)) → U11#(mark(X)) |
| active#(isNeList(__(V1, V2))) → isNeList#(V1) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(tt) → active#(tt) | mark#(o) → active#(o) |
| mark#(U11(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| mark#(U42(X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) → active#(isNePal(X)) | mark#(U81(X)) → U81#(mark(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| mark#(isList(X)) → isList#(X) | active#(U11(tt)) → mark#(tt) |
| mark#(u) → active#(u) | mark#(U52(X)) → active#(U52(mark(X))) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| active#(U72(tt)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | mark#(U22(X)) → mark#(X) |
| U72#(active(X)) → U72#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| isQid#(mark(X)) → isQid#(X) | isQid#(active(X)) → isQid#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(U51(tt, V2)) → U52#(isList(V2)) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | mark#(U61(X)) → U61#(mark(X)) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| mark#(U72(X)) → U72#(mark(X)) | active#(U71(tt, P)) → U72#(isPal(P)) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | mark#(U42(X)) → U42#(mark(X)) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | U72#(mark(X)) → U72#(X) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | U61#(active(X)) → U61#(X) |
| mark#(U31(X)) → mark#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | active#(U52(tt)) → mark#(tt) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | mark#(U11(X)) → U11#(mark(X)) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(isPal(X)) → isPal#(X) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| mark#(isList(X)) → isList#(X) | active#(U11(tt)) → mark#(tt) |
| mark#(U52(X)) → active#(U52(mark(X))) | mark#(u) → active#(u) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(U72(tt)) → mark#(tt) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(isQid(X)) → isQid#(X) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(U22(X)) → mark#(X) |
| U72#(active(X)) → U72#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| U72#(mark(X)) → U72#(X) | mark#(U72(X)) → U72#(mark(X)) |
| U72#(active(X)) → U72#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| active#(isList(__(V1, V2))) → isList#(V1) | mark#(U61(X)) → U61#(mark(X)) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| active#(U71(tt, P)) → U72#(isPal(P)) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U41(tt, V2)) → isNeList#(V2) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | U61#(active(X)) → U61#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U52(tt)) → mark#(tt) | active#(U42(tt)) → mark#(tt) |
| mark#(isNeList(X)) → isNeList#(X) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(isNeList(__(V1, V2))) → isNeList#(V1) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(tt) → active#(tt) | mark#(o) → active#(o) |
| mark#(U11(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| mark#(U42(X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(isNePal(X)) → active#(isNePal(X)) |
| mark#(U51(X1, X2)) → mark#(X1) | active#(U11(tt)) → mark#(tt) |
| mark#(u) → active#(u) | mark#(U52(X)) → active#(U52(mark(X))) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| active#(U72(tt)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(isList(V)) → U11#(isNeList(V)) | active#(__(nil, X)) → mark#(X) |
| mark#(U31(X)) → active#(U31(mark(X))) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | mark#(U22(X)) → mark#(X) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| __#(active(X1), X2) → __#(X1, X2) | __#(mark(X1), X2) → __#(X1, X2) |
| __#(X1, mark(X2)) → __#(X1, X2) | __#(X1, active(X2)) → __#(X1, X2) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | active#(__(X, nil)) → mark#(X) |
| mark#(U61(X)) → U61#(mark(X)) | mark#(a) → active#(a) |
| mark#(U72(X)) → U72#(mark(X)) | active#(U21(tt, V2)) → U22#(isList(V2)) |
| active#(U71(tt, P)) → U72#(isPal(P)) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| active#(U22(tt)) → mark#(tt) | mark#(i) → active#(i) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | mark#(U81(X)) → mark#(X) |
| active#(isQid(i)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(U42(X)) → U42#(mark(X)) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | mark#(U71(X1, X2)) → U71#(mark(X1), X2) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| U72#(mark(X)) → U72#(X) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | mark#(U31(X)) → mark#(X) |
| U61#(active(X)) → U61#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U52(tt)) → mark#(tt) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| mark#(U11(X)) → U11#(mark(X)) | active#(isNeList(__(V1, V2))) → isNeList#(V1) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| active#(U11(tt)) → mark#(tt) | mark#(U52(X)) → active#(U52(mark(X))) |
| mark#(u) → active#(u) | active#(isList(nil)) → mark#(tt) |
| active#(U61(tt)) → mark#(tt) | mark#(nil) → active#(nil) |
| mark#(U61(X)) → active#(U61(mark(X))) | mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(U31(X)) → active#(U31(mark(X))) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | mark#(U22(X)) → mark#(X) |
| U72#(active(X)) → U72#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | active#(__(X, nil)) → mark#(X) |
| mark#(U61(X)) → U61#(mark(X)) | mark#(a) → active#(a) |
| mark#(U72(X)) → U72#(mark(X)) | active#(U21(tt, V2)) → U22#(isList(V2)) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U42(X)) → U42#(mark(X)) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| U61#(active(X)) → U61#(X) | mark#(U31(X)) → mark#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(U52(tt)) → mark#(tt) |
| active#(isList(V)) → mark#(U11(isNeList(V))) | active#(U42(tt)) → mark#(tt) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | active#(isNeList(__(V1, V2))) → isNeList#(V1) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| mark#(U21(X1, X2)) → U21#(mark(X1), X2) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) → active#(isNePal(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) → mark#(X1) | active#(U11(tt)) → mark#(tt) |
| mark#(u) → active#(u) | mark#(U52(X)) → active#(U52(mark(X))) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(U72(tt)) → mark#(tt) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(isQid(X)) → isQid#(X) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(U22(X)) → mark#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| U22#(mark(X)) → U22#(X) | U22#(active(X)) → U22#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | mark#(U61(X)) → U61#(mark(X)) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| mark#(U72(X)) → U72#(mark(X)) | active#(U21(tt, V2)) → U22#(isList(V2)) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | mark#(U81(X)) → mark#(X) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U42(X)) → U42#(mark(X)) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| U61#(active(X)) → U61#(X) | mark#(U31(X)) → mark#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(U52(tt)) → mark#(tt) |
| active#(isList(V)) → mark#(U11(isNeList(V))) | active#(U42(tt)) → mark#(tt) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | active#(isNeList(__(V1, V2))) → isNeList#(V1) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(isPal(X)) → isPal#(X) | mark#(o) → active#(o) |
| mark#(U11(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| mark#(U42(X)) → mark#(X) | mark#(U21(X1, X2)) → U21#(mark(X1), X2) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| active#(U11(tt)) → mark#(tt) | mark#(U52(X)) → active#(U52(mark(X))) |
| mark#(u) → active#(u) | active#(isList(nil)) → mark#(tt) |
| active#(U61(tt)) → mark#(tt) | mark#(nil) → active#(nil) |
| mark#(U61(X)) → active#(U61(mark(X))) | mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(U31(X)) → active#(U31(mark(X))) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | active#(U51(tt, V2)) → isList#(V2) |
| mark#(U22(X)) → mark#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) → mark#(X) | mark#(U61(X)) → U61#(mark(X)) |
| mark#(a) → active#(a) | active#(U71(tt, P)) → U72#(isPal(P)) |
| mark#(U51(X1, X2)) → U51#(mark(X1), X2) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| active#(U22(tt)) → mark#(tt) | mark#(i) → active#(i) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | mark#(U81(X)) → mark#(X) |
| active#(isQid(i)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(isNePal(V)) → isQid#(V) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | mark#(U31(X)) → mark#(X) |
| U61#(active(X)) → U61#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U52(tt)) → mark#(tt) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| mark#(U81(X)) → U81#(mark(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) → mark#(X1) | mark#(isList(X)) → isList#(X) |
| active#(U11(tt)) → mark#(tt) | mark#(u) → active#(u) |
| mark#(U52(X)) → active#(U52(mark(X))) | active#(isList(nil)) → mark#(tt) |
| active#(U61(tt)) → mark#(tt) | mark#(nil) → active#(nil) |
| mark#(U61(X)) → active#(U61(mark(X))) | mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(U31(X)) → active#(U31(mark(X))) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | active#(U51(tt, V2)) → isList#(V2) |
| mark#(U22(X)) → mark#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(isQid(a)) → mark#(tt) |
| active#(U51(tt, V2)) → mark#(U52(isList(V2))) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| active#(U71(tt, P)) → U72#(isPal(P)) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U21(tt, V2)) → U22#(isList(V2)) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| active#(U22(tt)) → mark#(tt) | mark#(i) → active#(i) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | mark#(U81(X)) → mark#(X) |
| active#(isQid(i)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) → mark#(X) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U52(tt)) → mark#(tt) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | mark#(isNeList(X)) → isNeList#(X) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | active#(isNeList(__(V1, V2))) → isNeList#(V1) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(U81(X)) → U81#(mark(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(isNePal(X)) → active#(isNePal(X)) |
| mark#(U51(X1, X2)) → mark#(X1) | active#(U11(tt)) → mark#(tt) |
| mark#(u) → active#(u) | mark#(U52(X)) → active#(U52(mark(X))) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| mark#(U22(X)) → mark#(X) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(isList(__(V1, V2))) → isList#(V1) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | mark#(U61(X)) → U61#(mark(X)) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| mark#(U72(X)) → U72#(mark(X)) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U71(tt, P)) → U72#(isPal(P)) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| active#(U22(tt)) → mark#(tt) | mark#(i) → active#(i) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | mark#(U81(X)) → mark#(X) |
| active#(isQid(i)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(isNeList(V)) → U31#(isQid(V)) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| U72#(mark(X)) → U72#(X) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | mark#(U31(X)) → mark#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| active#(isList(V)) → mark#(U11(isNeList(V))) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U52(tt)) → mark#(tt) | active#(U42(tt)) → mark#(tt) |
| mark#(isNeList(X)) → isNeList#(X) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| mark#(isList(X)) → isList#(X) | active#(U11(tt)) → mark#(tt) |
| mark#(u) → active#(u) | mark#(U52(X)) → active#(U52(mark(X))) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| active#(__(__(X, Y), Z)) → __#(Y, Z) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(isQid(X)) → isQid#(X) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(U22(X)) → mark#(X) |
| U72#(active(X)) → U72#(X) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| active#(isList(__(V1, V2))) → isList#(V1) | mark#(U61(X)) → U61#(mark(X)) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| mark#(U72(X)) → U72#(mark(X)) | active#(U21(tt, V2)) → U22#(isList(V2)) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | mark#(U42(X)) → U42#(mark(X)) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) → mark#(X) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | U61#(active(X)) → U61#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U52(tt)) → mark#(tt) | active#(U42(tt)) → mark#(tt) |
| mark#(isNeList(X)) → isNeList#(X) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(U81(X)) → U81#(mark(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(isNePal(X)) → active#(isNePal(X)) |
| mark#(U51(X1, X2)) → mark#(X1) | active#(U11(tt)) → mark#(tt) |
| mark#(U52(X)) → active#(U52(mark(X))) | mark#(u) → active#(u) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(U72(tt)) → mark#(tt) |
| active#(isList(V)) → U11#(isNeList(V)) | active#(__(nil, X)) → mark#(X) |
| mark#(U31(X)) → active#(U31(mark(X))) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | mark#(U22(X)) → mark#(X) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) → mark#(X) | mark#(U61(X)) → U61#(mark(X)) |
| mark#(a) → active#(a) | active#(U71(tt, P)) → U72#(isPal(P)) |
| mark#(U51(X1, X2)) → U51#(mark(X1), X2) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| active#(U22(tt)) → mark#(tt) | mark#(i) → active#(i) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | mark#(U81(X)) → mark#(X) |
| active#(isQid(i)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(isNePal(V)) → isQid#(V) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | mark#(U31(X)) → mark#(X) |
| U61#(active(X)) → U61#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U52(tt)) → mark#(tt) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(isNeList(__(V1, V2))) → isNeList#(V1) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(tt) → active#(tt) | mark#(o) → active#(o) |
| mark#(U11(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| mark#(U42(X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) → active#(isNePal(X)) | mark#(U81(X)) → U81#(mark(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| mark#(isList(X)) → isList#(X) | active#(U11(tt)) → mark#(tt) |
| mark#(u) → active#(u) | mark#(U52(X)) → active#(U52(mark(X))) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(U72(tt)) → mark#(tt) |
| active#(__(nil, X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → isQid#(I) |
| mark#(U31(X)) → active#(U31(mark(X))) | mark#(isQid(X)) → isQid#(X) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(U22(X)) → mark#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| U72#(mark(X)) → U72#(X) | U72#(active(X)) → U72#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) → U61#(mark(X)) | active#(__(X, nil)) → mark#(X) |
| mark#(a) → active#(a) | mark#(U72(X)) → U72#(mark(X)) |
| mark#(U51(X1, X2)) → U51#(mark(X1), X2) | active#(U71(tt, P)) → U72#(isPal(P)) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| U72#(mark(X)) → U72#(X) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| active#(U21(tt, V2)) → isList#(V2) | U61#(active(X)) → U61#(X) |
| mark#(U31(X)) → mark#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | mark#(U22(X)) → U22#(mark(X)) |
| active#(U52(tt)) → mark#(tt) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(isList(V)) → mark#(U11(isNeList(V))) | active#(U42(tt)) → mark#(tt) |
| mark#(U11(X)) → U11#(mark(X)) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| mark#(isList(X)) → isList#(X) | active#(U11(tt)) → mark#(tt) |
| mark#(U52(X)) → active#(U52(mark(X))) | mark#(u) → active#(u) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(U72(tt)) → mark#(tt) |
| active#(__(nil, X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → isQid#(I) |
| mark#(U31(X)) → active#(U31(mark(X))) | mark#(isQid(X)) → isQid#(X) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(U22(X)) → mark#(X) |
| U72#(active(X)) → U72#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | active#(__(X, nil)) → mark#(X) |
| mark#(U61(X)) → U61#(mark(X)) | mark#(a) → active#(a) |
| mark#(U72(X)) → U72#(mark(X)) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U71(tt, P)) → U72#(isPal(P)) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| active#(U22(tt)) → mark#(tt) | mark#(i) → active#(i) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | mark#(U81(X)) → mark#(X) |
| active#(isQid(i)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(U42(X)) → U42#(mark(X)) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | U72#(mark(X)) → U72#(X) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | U61#(active(X)) → U61#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(U52(tt)) → mark#(tt) |
| active#(isList(V)) → mark#(U11(isNeList(V))) | active#(U42(tt)) → mark#(tt) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(isPal(X)) → isPal#(X) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| mark#(isList(X)) → isList#(X) | active#(U11(tt)) → mark#(tt) |
| mark#(U52(X)) → active#(U52(mark(X))) | mark#(u) → active#(u) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | active#(isPal(V)) → isNePal#(V) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(U31(X)) → active#(U31(mark(X))) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | active#(U51(tt, V2)) → isList#(V2) |
| mark#(U22(X)) → mark#(X) | U72#(active(X)) → U72#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| U71#(X1, active(X2)) → U71#(X1, X2) | U71#(active(X1), X2) → U71#(X1, X2) |
| U71#(mark(X1), X2) → U71#(X1, X2) | U71#(X1, mark(X2)) → U71#(X1, X2) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | active#(__(X, nil)) → mark#(X) |
| mark#(U61(X)) → U61#(mark(X)) | mark#(a) → active#(a) |
| mark#(U72(X)) → U72#(mark(X)) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U71(tt, P)) → U72#(isPal(P)) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| active#(U22(tt)) → mark#(tt) | mark#(i) → active#(i) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | mark#(U81(X)) → mark#(X) |
| active#(isQid(i)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(U42(X)) → U42#(mark(X)) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | U72#(mark(X)) → U72#(X) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | U61#(active(X)) → U61#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(U52(tt)) → mark#(tt) |
| active#(isList(V)) → mark#(U11(isNeList(V))) | active#(U42(tt)) → mark#(tt) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(isPal(X)) → isPal#(X) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| mark#(isList(X)) → isList#(X) | active#(U11(tt)) → mark#(tt) |
| mark#(U52(X)) → active#(U52(mark(X))) | mark#(u) → active#(u) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(U72(tt)) → mark#(tt) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(isQid(X)) → isQid#(X) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(U22(X)) → mark#(X) |
| U72#(active(X)) → U72#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) → U61#(mark(X)) | active#(__(X, nil)) → mark#(X) |
| mark#(a) → active#(a) | mark#(U72(X)) → U72#(mark(X)) |
| mark#(U51(X1, X2)) → U51#(mark(X1), X2) | active#(U71(tt, P)) → U72#(isPal(P)) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(isNePal(V)) → isQid#(V) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| U72#(mark(X)) → U72#(X) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U52(tt)) → mark#(tt) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| mark#(isList(X)) → isList#(X) | active#(U11(tt)) → mark#(tt) |
| mark#(u) → active#(u) | mark#(U52(X)) → active#(U52(mark(X))) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| mark#(U31(X)) → active#(U31(mark(X))) | active#(isNePal(__(I, __(P, I)))) → isQid#(I) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | active#(U51(tt, V2)) → isList#(V2) |
| mark#(U22(X)) → mark#(X) | U72#(active(X)) → U72#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | active#(__(X, nil)) → mark#(X) |
| mark#(U61(X)) → U61#(mark(X)) | mark#(a) → active#(a) |
| active#(U21(tt, V2)) → U22#(isList(V2)) | active#(U71(tt, P)) → U72#(isPal(P)) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U42(X)) → U42#(mark(X)) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| mark#(U71(X1, X2)) → U71#(mark(X1), X2) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | mark#(U31(X)) → mark#(X) |
| U61#(active(X)) → U61#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U52(tt)) → mark#(tt) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| mark#(U11(X)) → U11#(mark(X)) | active#(isNeList(__(V1, V2))) → isNeList#(V1) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U42(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| active#(U11(tt)) → mark#(tt) | mark#(U52(X)) → active#(U52(mark(X))) |
| mark#(u) → active#(u) | active#(isList(nil)) → mark#(tt) |
| active#(U61(tt)) → mark#(tt) | mark#(nil) → active#(nil) |
| mark#(U61(X)) → active#(U61(mark(X))) | mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| mark#(U31(X)) → active#(U31(mark(X))) | active#(isNePal(__(I, __(P, I)))) → isQid#(I) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | mark#(U22(X)) → mark#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | active#(__(X, nil)) → mark#(X) |
| mark#(U61(X)) → U61#(mark(X)) | mark#(a) → active#(a) |
| mark#(U72(X)) → U72#(mark(X)) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U21(tt, V2)) → U22#(isList(V2)) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| active#(U22(tt)) → mark#(tt) | mark#(i) → active#(i) |
| mark#(U81(X)) → mark#(X) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| active#(isQid(i)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(U42(X)) → U42#(mark(X)) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | U61#(active(X)) → U61#(X) |
| mark#(U31(X)) → mark#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | active#(U52(tt)) → mark#(tt) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | mark#(U11(X)) → U11#(mark(X)) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(tt) → active#(tt) | mark#(isPal(X)) → isPal#(X) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| mark#(U21(X1, X2)) → U21#(mark(X1), X2) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) → active#(isNePal(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) → mark#(X1) | active#(U11(tt)) → mark#(tt) |
| mark#(U52(X)) → active#(U52(mark(X))) | mark#(u) → active#(u) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | active#(isPal(V)) → isNePal#(V) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(U22(X)) → mark#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | active#(__(X, nil)) → mark#(X) |
| mark#(U61(X)) → U61#(mark(X)) | mark#(a) → active#(a) |
| active#(U21(tt, V2)) → U22#(isList(V2)) | active#(U71(tt, P)) → U72#(isPal(P)) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U42(X)) → U42#(mark(X)) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| mark#(U71(X1, X2)) → U71#(mark(X1), X2) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | mark#(U31(X)) → mark#(X) |
| U61#(active(X)) → U61#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U52(tt)) → mark#(tt) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| mark#(U11(X)) → U11#(mark(X)) | active#(isNeList(__(V1, V2))) → isNeList#(V1) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| mark#(U81(X)) → U81#(mark(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) → mark#(X1) | active#(U11(tt)) → mark#(tt) |
| mark#(U52(X)) → active#(U52(mark(X))) | mark#(u) → active#(u) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| active#(U72(tt)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(isQid(X)) → isQid#(X) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| mark#(U22(X)) → mark#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| isList#(active(X)) → isList#(X) | isList#(mark(X)) → isList#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | mark#(U61(X)) → U61#(mark(X)) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| mark#(U72(X)) → U72#(mark(X)) | active#(U21(tt, V2)) → U22#(isList(V2)) |
| active#(U71(tt, P)) → U72#(isPal(P)) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| active#(U22(tt)) → mark#(tt) | mark#(i) → active#(i) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | mark#(U81(X)) → mark#(X) |
| active#(isQid(i)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(U42(X)) → U42#(mark(X)) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | mark#(U71(X1, X2)) → U71#(mark(X1), X2) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| U72#(mark(X)) → U72#(X) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | mark#(U31(X)) → mark#(X) |
| U61#(active(X)) → U61#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U52(tt)) → mark#(tt) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| mark#(U11(X)) → U11#(mark(X)) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(tt) → active#(tt) | mark#(o) → active#(o) |
| mark#(U11(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| mark#(U42(X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) → active#(isNePal(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) → mark#(X1) | active#(U11(tt)) → mark#(tt) |
| mark#(U52(X)) → active#(U52(mark(X))) | mark#(u) → active#(u) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(U72(tt)) → mark#(tt) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(isQid(X)) → isQid#(X) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(U22(X)) → mark#(X) |
| U72#(active(X)) → U72#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(U51(tt, V2)) → U52#(isList(V2)) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | active#(__(X, nil)) → mark#(X) |
| mark#(U61(X)) → U61#(mark(X)) | mark#(a) → active#(a) |
| active#(U21(tt, V2)) → U22#(isList(V2)) | active#(U71(tt, P)) → U72#(isPal(P)) |
| mark#(U51(X1, X2)) → U51#(mark(X1), X2) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| active#(U22(tt)) → mark#(tt) | mark#(i) → active#(i) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | mark#(U81(X)) → mark#(X) |
| active#(isQid(i)) → mark#(tt) | U22#(mark(X)) → U22#(X) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | U61#(active(X)) → U61#(X) |
| mark#(U31(X)) → mark#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | U22#(active(X)) → U22#(X) |
| mark#(U22(X)) → U22#(mark(X)) | active#(U52(tt)) → mark#(tt) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | mark#(U11(X)) → U11#(mark(X)) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(tt) → active#(tt) | mark#(o) → active#(o) |
| mark#(U11(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| mark#(U42(X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) → active#(isNePal(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) → mark#(X1) | mark#(isList(X)) → isList#(X) |
| active#(U11(tt)) → mark#(tt) | mark#(u) → active#(u) |
| mark#(U52(X)) → active#(U52(mark(X))) | active#(isList(nil)) → mark#(tt) |
| active#(U61(tt)) → mark#(tt) | mark#(nil) → active#(nil) |
| mark#(U61(X)) → active#(U61(mark(X))) | mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| mark#(U31(X)) → active#(U31(mark(X))) | active#(isNePal(__(I, __(P, I)))) → isQid#(I) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | mark#(U22(X)) → mark#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| U21#(X1, mark(X2)) → U21#(X1, X2) | U21#(mark(X1), X2) → U21#(X1, X2) |
| U21#(active(X1), X2) → U21#(X1, X2) | U21#(X1, active(X2)) → U21#(X1, X2) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(U51(tt, V2)) → U52#(isList(V2)) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | mark#(U61(X)) → U61#(mark(X)) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| mark#(U72(X)) → U72#(mark(X)) | active#(U71(tt, P)) → U72#(isPal(P)) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | mark#(U42(X)) → U42#(mark(X)) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | U72#(mark(X)) → U72#(X) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | active#(U21(tt, V2)) → isList#(V2) |
| U61#(active(X)) → U61#(X) | mark#(U31(X)) → mark#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| active#(U52(tt)) → mark#(tt) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(isList(V)) → mark#(U11(isNeList(V))) | active#(U42(tt)) → mark#(tt) |
| mark#(U11(X)) → U11#(mark(X)) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| mark#(isList(X)) → isList#(X) | active#(U11(tt)) → mark#(tt) |
| mark#(U52(X)) → active#(U52(mark(X))) | mark#(u) → active#(u) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(U72(tt)) → mark#(tt) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | mark#(U22(X)) → mark#(X) |
| U72#(active(X)) → U72#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| active#(isList(__(V1, V2))) → isList#(V1) | mark#(U61(X)) → U61#(mark(X)) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| active#(U71(tt, P)) → U72#(isPal(P)) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U41(tt, V2)) → isNeList#(V2) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | U61#(active(X)) → U61#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U52(tt)) → mark#(tt) | active#(U42(tt)) → mark#(tt) |
| mark#(isNeList(X)) → isNeList#(X) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(U81(X)) → U81#(mark(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(isNePal(X)) → active#(isNePal(X)) |
| mark#(U51(X1, X2)) → mark#(X1) | active#(U11(tt)) → mark#(tt) |
| mark#(u) → active#(u) | mark#(U52(X)) → active#(U52(mark(X))) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| active#(U72(tt)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(isList(V)) → U11#(isNeList(V)) | active#(__(nil, X)) → mark#(X) |
| mark#(U31(X)) → active#(U31(mark(X))) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | mark#(U22(X)) → mark#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | mark#(U61(X)) → U61#(mark(X)) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| mark#(U72(X)) → U72#(mark(X)) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U42(X)) → U42#(mark(X)) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | U61#(active(X)) → U61#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U52(tt)) → mark#(tt) | active#(U42(tt)) → mark#(tt) |
| mark#(U11(X)) → U11#(mark(X)) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(isPal(X)) → isPal#(X) |
| mark#(tt) → active#(tt) | mark#(o) → active#(o) |
| mark#(U11(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| mark#(U42(X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) → active#(isNePal(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) → mark#(X1) | mark#(isList(X)) → isList#(X) |
| active#(U11(tt)) → mark#(tt) | mark#(u) → active#(u) |
| mark#(U52(X)) → active#(U52(mark(X))) | active#(isList(nil)) → mark#(tt) |
| active#(U61(tt)) → mark#(tt) | mark#(nil) → active#(nil) |
| mark#(U61(X)) → active#(U61(mark(X))) | mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| mark#(U31(X)) → active#(U31(mark(X))) | active#(isNePal(__(I, __(P, I)))) → isQid#(I) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | active#(U51(tt, V2)) → isList#(V2) |
| mark#(U22(X)) → mark#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) → U61#(mark(X)) | active#(__(X, nil)) → mark#(X) |
| mark#(a) → active#(a) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U71(tt, P)) → U72#(isPal(P)) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| U51#(mark(X1), X2) → U51#(X1, X2) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | U61#(active(X)) → U61#(X) |
| mark#(U31(X)) → mark#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| mark#(U22(X)) → U22#(mark(X)) | active#(U52(tt)) → mark#(tt) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(U42(tt)) → mark#(tt) |
| mark#(U11(X)) → U11#(mark(X)) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| U51#(X1, active(X2)) → U51#(X1, X2) | active#(isNeList(__(V1, V2))) → isNeList#(V1) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| U51#(active(X1), X2) → U51#(X1, X2) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) → active#(isNePal(X)) | mark#(U81(X)) → U81#(mark(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| mark#(isList(X)) → isList#(X) | active#(U11(tt)) → mark#(tt) |
| mark#(u) → active#(u) | mark#(U52(X)) → active#(U52(mark(X))) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U61(X)) → mark#(X) | active#(isNeList(__(V1, V2))) → U51#(isNeList(V1), V2) |
| active#(isQid(o)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| mark#(U31(X)) → active#(U31(mark(X))) | active#(isNePal(__(I, __(P, I)))) → isQid#(I) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | U51#(X1, mark(X2)) → U51#(X1, X2) |
| mark#(U22(X)) → mark#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) → U61#(mark(X)) | active#(__(X, nil)) → mark#(X) |
| mark#(a) → active#(a) | active#(U21(tt, V2)) → U22#(isList(V2)) |
| active#(U71(tt, P)) → U72#(isPal(P)) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | mark#(U31(X)) → mark#(X) |
| U61#(active(X)) → U61#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(isList(V)) → mark#(U11(isNeList(V))) | active#(U52(tt)) → mark#(tt) |
| active#(U42(tt)) → mark#(tt) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(U81(X)) → U81#(mark(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(isNePal(X)) → active#(isNePal(X)) |
| mark#(U51(X1, X2)) → mark#(X1) | mark#(isList(X)) → isList#(X) |
| active#(U11(tt)) → mark#(tt) | mark#(U52(X)) → active#(U52(mark(X))) |
| mark#(u) → active#(u) | active#(isList(nil)) → mark#(tt) |
| active#(U61(tt)) → mark#(tt) | mark#(nil) → active#(nil) |
| mark#(U61(X)) → active#(U61(mark(X))) | mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | active#(U72(tt)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(__(nil, X)) → mark#(X) |
| mark#(U31(X)) → active#(U31(mark(X))) | active#(isNePal(__(I, __(P, I)))) → isQid#(I) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | active#(U51(tt, V2)) → isList#(V2) |
| mark#(U22(X)) → mark#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) → mark#(X) | mark#(U61(X)) → U61#(mark(X)) |
| mark#(a) → active#(a) | mark#(U72(X)) → U72#(mark(X)) |
| active#(U21(tt, V2)) → U22#(isList(V2)) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | mark#(U81(X)) → mark#(X) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(U21(tt, V2)) → isList#(V2) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | U61#(active(X)) → U61#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| active#(isList(V)) → mark#(U11(isNeList(V))) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U52(tt)) → mark#(tt) | active#(U42(tt)) → mark#(tt) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | mark#(U11(X)) → U11#(mark(X)) |
| active#(isNeList(__(V1, V2))) → isNeList#(V1) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(tt) → active#(tt) | mark#(o) → active#(o) |
| mark#(U11(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| mark#(U21(X1, X2)) → U21#(mark(X1), X2) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(isNePal(X)) → active#(isNePal(X)) | mark#(U51(X1, X2)) → mark#(X1) |
| active#(U11(tt)) → mark#(tt) | mark#(U52(X)) → active#(U52(mark(X))) |
| mark#(u) → active#(u) | active#(U61(tt)) → mark#(tt) |
| active#(isList(nil)) → mark#(tt) | mark#(nil) → active#(nil) |
| mark#(U61(X)) → active#(U61(mark(X))) | mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | active#(U72(tt)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(__(nil, X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(U31(X)) → active#(U31(mark(X))) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | mark#(U22(X)) → mark#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| isNePal#(active(X)) → isNePal#(X) | isNePal#(mark(X)) → isNePal#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) → mark#(X) | mark#(U61(X)) → U61#(mark(X)) |
| mark#(a) → active#(a) | mark#(U72(X)) → U72#(mark(X)) |
| mark#(U51(X1, X2)) → U51#(mark(X1), X2) | active#(U71(tt, P)) → U72#(isPal(P)) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(isNePal(V)) → isQid#(V) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | U72#(mark(X)) → U72#(X) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(U52(tt)) → mark#(tt) |
| active#(U42(tt)) → mark#(tt) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| mark#(isList(X)) → isList#(X) | active#(U11(tt)) → mark#(tt) |
| mark#(u) → active#(u) | mark#(U52(X)) → active#(U52(mark(X))) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| mark#(U31(X)) → active#(U31(mark(X))) | mark#(isQid(X)) → isQid#(X) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(U22(X)) → mark#(X) |
| U72#(active(X)) → U72#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| active#(isList(__(V1, V2))) → isList#(V1) | mark#(U61(X)) → U61#(mark(X)) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| active#(U71(tt, P)) → U72#(isPal(P)) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U41(tt, V2)) → isNeList#(V2) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | U61#(active(X)) → U61#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U52(tt)) → mark#(tt) | active#(U42(tt)) → mark#(tt) |
| mark#(isNeList(X)) → isNeList#(X) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(isNeList(__(V1, V2))) → isNeList#(V1) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(tt) → active#(tt) | mark#(o) → active#(o) |
| mark#(U11(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| mark#(U42(X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| mark#(U81(X)) → U81#(mark(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(isNePal(X)) → active#(isNePal(X)) | mark#(U51(X1, X2)) → mark#(X1) |
| active#(U11(tt)) → mark#(tt) | mark#(u) → active#(u) |
| mark#(U52(X)) → active#(U52(mark(X))) | active#(isList(nil)) → mark#(tt) |
| active#(U61(tt)) → mark#(tt) | mark#(nil) → active#(nil) |
| mark#(U61(X)) → active#(U61(mark(X))) | mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | active#(U72(tt)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(isList(V)) → U11#(isNeList(V)) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| mark#(U22(X)) → mark#(X) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | active#(__(X, nil)) → mark#(X) |
| mark#(U61(X)) → U61#(mark(X)) | mark#(a) → active#(a) |
| active#(U21(tt, V2)) → U22#(isList(V2)) | active#(U71(tt, P)) → U72#(isPal(P)) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U42(X)) → U42#(mark(X)) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | U61#(active(X)) → U61#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(U52(tt)) → mark#(tt) |
| active#(isList(V)) → mark#(U11(isNeList(V))) | active#(U42(tt)) → mark#(tt) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | active#(isNeList(__(V1, V2))) → isNeList#(V1) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| mark#(U81(X)) → U81#(mark(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) → mark#(X1) | active#(U11(tt)) → mark#(tt) |
| mark#(U52(X)) → active#(U52(mark(X))) | mark#(u) → active#(u) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(U72(tt)) → mark#(tt) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(isQid(X)) → isQid#(X) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(U22(X)) → mark#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) → U61#(mark(X)) | active#(__(X, nil)) → mark#(X) |
| mark#(a) → active#(a) | mark#(U72(X)) → U72#(mark(X)) |
| active#(U21(tt, V2)) → U22#(isList(V2)) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | mark#(U81(X)) → mark#(X) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | mark#(U31(X)) → mark#(X) |
| U61#(active(X)) → U61#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U52(tt)) → mark#(tt) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | mark#(U11(X)) → U11#(mark(X)) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | active#(isNeList(__(V1, V2))) → isNeList#(V1) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| mark#(U21(X1, X2)) → U21#(mark(X1), X2) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) → active#(isNePal(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) → mark#(X1) | mark#(isList(X)) → isList#(X) |
| active#(U11(tt)) → mark#(tt) | mark#(U52(X)) → active#(U52(mark(X))) |
| mark#(u) → active#(u) | active#(U61(tt)) → mark#(tt) |
| active#(isList(nil)) → mark#(tt) | mark#(nil) → active#(nil) |
| mark#(U61(X)) → active#(U61(mark(X))) | mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(U31(X)) → active#(U31(mark(X))) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | active#(U51(tt, V2)) → isList#(V2) |
| mark#(U22(X)) → mark#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | mark#(U61(X)) → U61#(mark(X)) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| mark#(U72(X)) → U72#(mark(X)) | active#(U21(tt, V2)) → U22#(isList(V2)) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U42(X)) → U42#(mark(X)) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| mark#(U71(X1, X2)) → U71#(mark(X1), X2) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | mark#(U31(X)) → mark#(X) |
| U61#(active(X)) → U61#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U52(tt)) → mark#(tt) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| mark#(U11(X)) → U11#(mark(X)) | active#(isNeList(__(V1, V2))) → isNeList#(V1) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(isPal(X)) → isPal#(X) | mark#(o) → active#(o) |
| mark#(U11(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| mark#(U42(X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) → active#(isNePal(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) → mark#(X1) | active#(U11(tt)) → mark#(tt) |
| mark#(U52(X)) → active#(U52(mark(X))) | mark#(u) → active#(u) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(U72(tt)) → mark#(tt) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(isQid(X)) → isQid#(X) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(U22(X)) → mark#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) → mark#(X) | mark#(U61(X)) → U61#(mark(X)) |
| mark#(a) → active#(a) | active#(U71(tt, P)) → U72#(isPal(P)) |
| mark#(U51(X1, X2)) → U51#(mark(X1), X2) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| active#(U22(tt)) → mark#(tt) | mark#(i) → active#(i) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | mark#(U81(X)) → mark#(X) |
| active#(isQid(i)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| U61#(active(X)) → U61#(X) | mark#(U31(X)) → mark#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| active#(isList(V)) → mark#(U11(isNeList(V))) | active#(U52(tt)) → mark#(tt) |
| mark#(U22(X)) → U22#(mark(X)) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U42(tt)) → mark#(tt) | mark#(isNeList(X)) → isNeList#(X) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | active#(isNeList(__(V1, V2))) → isNeList#(V1) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| mark#(isList(X)) → isList#(X) | active#(U11(tt)) → mark#(tt) |
| mark#(u) → active#(u) | mark#(U52(X)) → active#(U52(mark(X))) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) |
| mark#(U61(X)) → active#(U61(mark(X))) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(U72(tt)) → mark#(tt) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(isQid(X)) → isQid#(X) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(U22(X)) → mark#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | mark#(U61(X)) → U61#(mark(X)) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| mark#(U72(X)) → U72#(mark(X)) | active#(U71(tt, P)) → U72#(isPal(P)) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U42(X)) → U42#(mark(X)) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| mark#(U71(X1, X2)) → U71#(mark(X1), X2) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(U71(X1, X2)) → mark#(X1) | mark#(isQid(X)) → active#(isQid(X)) |
| active#(U31(tt)) → mark#(tt) | U72#(mark(X)) → U72#(X) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | U61#(active(X)) → U61#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(U52(tt)) → mark#(tt) |
| active#(isList(V)) → mark#(U11(isNeList(V))) | active#(U42(tt)) → mark#(tt) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | mark#(U11(X)) → U11#(mark(X)) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(isPal(X)) → isPal#(X) |
| mark#(tt) → active#(tt) | mark#(o) → active#(o) |
| mark#(U11(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| mark#(U42(X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) → active#(isNePal(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) → mark#(X1) | active#(U11(tt)) → mark#(tt) |
| mark#(u) → active#(u) | mark#(U52(X)) → active#(U52(mark(X))) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(U72(tt)) → mark#(tt) |
| active#(__(nil, X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → isQid#(I) |
| mark#(U31(X)) → active#(U31(mark(X))) | mark#(isNePal(X)) → isNePal#(X) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | active#(U51(tt, V2)) → isList#(V2) |
| mark#(U22(X)) → mark#(X) | U72#(active(X)) → U72#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| U81#(mark(X)) → U81#(X) | active#(isPal(V)) → U81#(isNePal(V)) |
| U81#(active(X)) → U81#(X) |
| U81#(mark(X)) → U81#(X) | U81#(active(X)) → U81#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | active#(__(X, nil)) → mark#(X) |
| mark#(U61(X)) → U61#(mark(X)) | mark#(a) → active#(a) |
| mark#(U51(X1, X2)) → U51#(mark(X1), X2) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| active#(U22(tt)) → mark#(tt) | mark#(i) → active#(i) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | mark#(U81(X)) → mark#(X) |
| active#(isQid(i)) → mark#(tt) | active#(isPal(V)) → U81#(isNePal(V)) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U42(X)) → U42#(mark(X)) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(isNePal(V)) → isQid#(V) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | mark#(U31(X)) → mark#(X) |
| U61#(active(X)) → U61#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U52(tt)) → mark#(tt) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U42(tt)) → mark#(tt) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| mark#(U11(X)) → U11#(mark(X)) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(tt) → active#(tt) | mark#(isPal(X)) → isPal#(X) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U21(X1, X2)) → U21#(mark(X1), X2) |
| mark#(U42(X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(isNePal(X)) → active#(isNePal(X)) |
| mark#(U51(X1, X2)) → mark#(X1) | mark#(isList(X)) → isList#(X) |
| active#(U11(tt)) → mark#(tt) | mark#(U52(X)) → active#(U52(mark(X))) |
| mark#(u) → active#(u) | active#(U61(tt)) → mark#(tt) |
| active#(isList(nil)) → mark#(tt) | mark#(nil) → active#(nil) |
| mark#(U61(X)) → active#(U61(mark(X))) | mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| mark#(U31(X)) → active#(U31(mark(X))) | active#(isNePal(__(I, __(P, I)))) → isQid#(I) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(isList(X)) → active#(isList(X)) |
| mark#(U22(X)) → mark#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) → U61#(mark(X)) | active#(__(X, nil)) → mark#(X) |
| mark#(a) → active#(a) | mark#(U72(X)) → U72#(mark(X)) |
| active#(U21(tt, V2)) → U22#(isList(V2)) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| active#(U22(tt)) → mark#(tt) | mark#(i) → active#(i) |
| mark#(U81(X)) → mark#(X) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| active#(isQid(i)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| active#(U21(tt, V2)) → isList#(V2) | mark#(U31(X)) → mark#(X) |
| U61#(active(X)) → U61#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U52(tt)) → mark#(tt) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | mark#(U11(X)) → U11#(mark(X)) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | active#(isNeList(__(V1, V2))) → isNeList#(V1) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| mark#(U21(X1, X2)) → U21#(mark(X1), X2) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(isNePal(X)) → active#(isNePal(X)) |
| mark#(U51(X1, X2)) → mark#(X1) | active#(U11(tt)) → mark#(tt) |
| mark#(U52(X)) → active#(U52(mark(X))) | mark#(u) → active#(u) |
| active#(U61(tt)) → mark#(tt) | active#(isList(nil)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(U72(tt)) → mark#(tt) |
| active#(__(nil, X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → isQid#(I) |
| mark#(U31(X)) → active#(U31(mark(X))) | mark#(isQid(X)) → isQid#(X) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(U22(X)) → mark#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(U51(tt, V2)) → U52#(isList(V2)) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | mark#(U61(X)) → U61#(mark(X)) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| mark#(U51(X1, X2)) → U51#(mark(X1), X2) | active#(U71(tt, P)) → U72#(isPal(P)) |
| active#(U21(tt, V2)) → U22#(isList(V2)) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| active#(U22(tt)) → mark#(tt) | mark#(i) → active#(i) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | mark#(U81(X)) → mark#(X) |
| active#(isQid(i)) → mark#(tt) | U22#(mark(X)) → U22#(X) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | U61#(active(X)) → U61#(X) |
| mark#(U31(X)) → mark#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | U22#(active(X)) → U22#(X) |
| mark#(U22(X)) → U22#(mark(X)) | active#(U52(tt)) → mark#(tt) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | mark#(U11(X)) → U11#(mark(X)) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(tt) → active#(tt) | mark#(o) → active#(o) |
| mark#(U11(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| mark#(U42(X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) → active#(isNePal(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) → mark#(X1) | active#(U11(tt)) → mark#(tt) |
| mark#(u) → active#(u) | mark#(U52(X)) → active#(U52(mark(X))) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(U72(tt)) → mark#(tt) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(isQid(X)) → isQid#(X) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| mark#(U22(X)) → mark#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| isPal#(mark(X)) → isPal#(X) | isPal#(active(X)) → isPal#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | active#(__(X, nil)) → mark#(X) |
| mark#(a) → active#(a) | active#(U71(tt, P)) → U72#(isPal(P)) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U81(tt)) → mark#(tt) |
| active#(isNeList(V)) → U31#(isQid(V)) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(U21(tt, V2)) → isList#(V2) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | mark#(U31(X)) → mark#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| active#(U52(tt)) → mark#(tt) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(isList(V)) → mark#(U11(isNeList(V))) | active#(U42(tt)) → mark#(tt) |
| active#(isList(__(V1, V2))) → U21#(isList(V1), V2) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(isNeList(__(V1, V2))) → isNeList#(V1) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(isPal(X)) → isPal#(X) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| mark#(isList(X)) → isList#(X) | active#(U11(tt)) → mark#(tt) |
| mark#(U52(X)) → active#(U52(mark(X))) | mark#(u) → active#(u) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | active#(isPal(V)) → isNePal#(V) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | active#(U72(tt)) → mark#(tt) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | mark#(U22(X)) → mark#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| U61#(mark(X)) → U61#(X) | U61#(active(X)) → U61#(X) |
| U52#(active(X)) → U52#(X) | U52#(mark(X)) → U52#(X) |
| U42#(mark(X)) → U42#(X) | U42#(active(X)) → U42#(X) |
| U11#(active(X)) → U11#(X) | U11#(mark(X)) → U11#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | mark#(U61(X)) → U61#(mark(X)) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| mark#(U72(X)) → U72#(mark(X)) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U42(X)) → U42#(mark(X)) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(isNePal(V)) → isQid#(V) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(U52(tt)) → mark#(tt) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U42(tt)) → mark#(tt) | mark#(U11(X)) → U11#(mark(X)) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(isPal(X)) → isPal#(X) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(isNePal(X)) → active#(isNePal(X)) | mark#(U51(X1, X2)) → mark#(X1) |
| mark#(isList(X)) → isList#(X) | active#(U11(tt)) → mark#(tt) |
| mark#(U52(X)) → active#(U52(mark(X))) | mark#(u) → active#(u) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| mark#(U31(X)) → active#(U31(mark(X))) | mark#(isQid(X)) → isQid#(X) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(U22(X)) → mark#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(U51(tt, V2)) → U52#(isList(V2)) | active#(isQid(a)) → mark#(tt) |
| active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) | mark#(U61(X)) → U61#(mark(X)) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| mark#(U72(X)) → U72#(mark(X)) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U42(X)) → U42#(mark(X)) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | U61#(active(X)) → U61#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U52(tt)) → mark#(tt) | active#(U42(tt)) → mark#(tt) |
| mark#(U11(X)) → U11#(mark(X)) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(isPal(X)) → isPal#(X) | mark#(o) → active#(o) |
| mark#(U11(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| mark#(U42(X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) → active#(isNePal(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) → mark#(X1) | active#(U11(tt)) → mark#(tt) |
| mark#(U52(X)) → active#(U52(mark(X))) | mark#(u) → active#(u) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| active#(U72(tt)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(isQid(X)) → isQid#(X) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(U22(X)) → mark#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| U31#(active(X)) → U31#(X) | U31#(mark(X)) → U31#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| active#(isList(__(V1, V2))) → isList#(V1) | mark#(U61(X)) → U61#(mark(X)) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| mark#(U51(X1, X2)) → U51#(mark(X1), X2) | active#(U71(tt, P)) → U72#(isPal(P)) |
| active#(U21(tt, V2)) → U22#(isList(V2)) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| active#(U22(tt)) → mark#(tt) | mark#(i) → active#(i) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | mark#(U81(X)) → mark#(X) |
| active#(isQid(i)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(U41(tt, V2)) → isNeList#(V2) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | mark#(U31(X)) → mark#(X) |
| U61#(active(X)) → U61#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | mark#(U22(X)) → active#(U22(mark(X))) |
| active#(isList(V)) → mark#(U11(isNeList(V))) | active#(U52(tt)) → mark#(tt) |
| active#(U42(tt)) → mark#(tt) | mark#(isNeList(X)) → isNeList#(X) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | active#(isNeList(__(V1, V2))) → isNeList#(V1) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U42(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| mark#(U81(X)) → U81#(mark(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) → mark#(X1) | active#(U11(tt)) → mark#(tt) |
| mark#(u) → active#(u) | mark#(U52(X)) → active#(U52(mark(X))) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(U72(tt)) → mark#(tt) |
| active#(isList(V)) → U11#(isNeList(V)) | active#(__(nil, X)) → mark#(X) |
| mark#(U31(X)) → active#(U31(mark(X))) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | mark#(U22(X)) → mark#(X) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) → U61#(mark(X)) | active#(__(X, nil)) → mark#(X) |
| mark#(a) → active#(a) | mark#(U72(X)) → U72#(mark(X)) |
| active#(U71(tt, P)) → U72#(isPal(P)) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| U72#(mark(X)) → U72#(X) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| active#(U21(tt, V2)) → isList#(V2) | mark#(U31(X)) → mark#(X) |
| U61#(active(X)) → U61#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(U52(tt)) → mark#(tt) |
| active#(U42(tt)) → mark#(tt) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| mark#(isList(X)) → isList#(X) | active#(U11(tt)) → mark#(tt) |
| mark#(U52(X)) → active#(U52(mark(X))) | mark#(u) → active#(u) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| active#(U72(tt)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | mark#(isQid(X)) → isQid#(X) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(U22(X)) → mark#(X) |
| U72#(active(X)) → U72#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| U51#(X1, mark(X2)) → U51#(X1, X2) | U51#(mark(X1), X2) → U51#(X1, X2) |
| U51#(X1, active(X2)) → U51#(X1, X2) | U51#(active(X1), X2) → U51#(X1, X2) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) → U61#(mark(X)) | active#(__(X, nil)) → mark#(X) |
| mark#(a) → active#(a) | mark#(U72(X)) → U72#(mark(X)) |
| active#(U71(tt, P)) → U72#(isPal(P)) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X2) | mark#(U72(X)) → active#(U72(mark(X))) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | U72#(mark(X)) → U72#(X) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | U61#(active(X)) → U61#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(U52(tt)) → mark#(tt) |
| active#(isList(V)) → mark#(U11(isNeList(V))) | active#(U42(tt)) → mark#(tt) |
| mark#(U11(X)) → U11#(mark(X)) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| mark#(isList(X)) → isList#(X) | active#(U11(tt)) → mark#(tt) |
| mark#(u) → active#(u) | mark#(U52(X)) → active#(U52(mark(X))) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| active#(U72(tt)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | active#(U51(tt, V2)) → isList#(V2) |
| mark#(U22(X)) → mark#(X) | U72#(active(X)) → U72#(X) |
| active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) | active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) → U61#(mark(X)) | active#(__(X, nil)) → mark#(X) |
| mark#(a) → active#(a) | active#(U71(tt, P)) → U72#(isPal(P)) |
| mark#(U51(X1, X2)) → U51#(mark(X1), X2) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| active#(U22(tt)) → mark#(tt) | mark#(i) → active#(i) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | mark#(U81(X)) → mark#(X) |
| active#(isQid(i)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | U61#(active(X)) → U61#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| active#(U52(tt)) → mark#(tt) | active#(U42(tt)) → mark#(tt) |
| mark#(isNeList(X)) → isNeList#(X) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(isNeList(__(V1, V2))) → isNeList#(V1) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(tt) → active#(tt) | mark#(o) → active#(o) |
| mark#(U11(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| mark#(U42(X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| mark#(U81(X)) → U81#(mark(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(isNePal(X)) → active#(isNePal(X)) | mark#(U51(X1, X2)) → mark#(X1) |
| active#(U11(tt)) → mark#(tt) | mark#(u) → active#(u) |
| mark#(U52(X)) → active#(U52(mark(X))) | active#(isList(nil)) → mark#(tt) |
| active#(U61(tt)) → mark#(tt) | mark#(nil) → active#(nil) |
| mark#(U61(X)) → active#(U61(mark(X))) | mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(U72(tt)) → mark#(tt) | active#(__(nil, X)) → mark#(X) |
| mark#(U31(X)) → active#(U31(mark(X))) | active#(isNePal(__(I, __(P, I)))) → isQid#(I) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| active#(U51(tt, V2)) → isList#(V2) | mark#(U22(X)) → mark#(X) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| mark#(U61(X)) → U61#(mark(X)) | active#(__(X, nil)) → mark#(X) |
| mark#(a) → active#(a) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U71(tt, P)) → U72#(isPal(P)) | active#(U21(tt, V2)) → mark#(U22(isList(V2))) |
| mark#(e) → active#(e) | mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) |
| active#(U22(tt)) → mark#(tt) | mark#(i) → active#(i) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | mark#(U81(X)) → mark#(X) |
| active#(isQid(i)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(isNePal(V)) → isQid#(V) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(U52(X)) → mark#(X) | mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → U61#(isQid(V)) |
| active#(isNePal(V)) → mark#(U61(isQid(V))) | U61#(active(X)) → U61#(X) |
| mark#(U31(X)) → mark#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| mark#(U22(X)) → U22#(mark(X)) | active#(U52(tt)) → mark#(tt) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(U42(tt)) → mark#(tt) |
| mark#(isNeList(X)) → isNeList#(X) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(isNeList(__(V1, V2))) → isNeList#(V1) | active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) |
| mark#(tt) → active#(tt) | mark#(o) → active#(o) |
| mark#(U11(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| mark#(U42(X)) → mark#(X) | active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) |
| mark#(isNePal(X)) → active#(isNePal(X)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(U51(X1, X2)) → mark#(X1) | mark#(isList(X)) → isList#(X) |
| active#(U11(tt)) → mark#(tt) | mark#(u) → active#(u) |
| mark#(U52(X)) → active#(U52(mark(X))) | active#(isList(nil)) → mark#(tt) |
| active#(U61(tt)) → mark#(tt) | mark#(nil) → active#(nil) |
| mark#(U61(X)) → active#(U61(mark(X))) | mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | active#(U72(tt)) → mark#(tt) |
| U61#(mark(X)) → U61#(X) | active#(__(nil, X)) → mark#(X) |
| mark#(U31(X)) → active#(U31(mark(X))) | active#(isNePal(__(I, __(P, I)))) → isQid#(I) |
| mark#(isQid(X)) → isQid#(X) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | active#(U51(tt, V2)) → isList#(V2) |
| mark#(U22(X)) → mark#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) → mark#(X) | mark#(U61(X)) → U61#(mark(X)) |
| mark#(a) → active#(a) | active#(U21(tt, V2)) → U22#(isList(V2)) |
| active#(U71(tt, P)) → U72#(isPal(P)) | mark#(U51(X1, X2)) → U51#(mark(X1), X2) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | active#(U71(tt, P)) → mark#(U72(isPal(P))) |
| mark#(U81(X)) → mark#(X) | active#(isQid(i)) → mark#(tt) |
| U22#(mark(X)) → U22#(X) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(U72(X)) → mark#(X) |
| active#(isQid(e)) → mark#(tt) | mark#(U81(X)) → active#(U81(mark(X))) |
| active#(U81(tt)) → mark#(tt) | mark#(isPal(X)) → active#(isPal(X)) |
| mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) | mark#(U52(X)) → mark#(X) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(isQid(X)) → active#(isQid(X)) |
| mark#(U71(X1, X2)) → mark#(X1) | active#(U31(tt)) → mark#(tt) |
| mark#(U42(X)) → active#(U42(mark(X))) | mark#(isNeList(X)) → active#(isNeList(X)) |
| active#(isNePal(V)) → U61#(isQid(V)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | U61#(active(X)) → U61#(X) |
| active#(isPal(nil)) → mark#(tt) | mark#(__(X1, X2)) → mark#(X1) |
| U22#(active(X)) → U22#(X) | mark#(U22(X)) → active#(U22(mark(X))) |
| mark#(U22(X)) → U22#(mark(X)) | active#(U52(tt)) → mark#(tt) |
| active#(isList(V)) → mark#(U11(isNeList(V))) | active#(U42(tt)) → mark#(tt) |
| active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) | active#(isNeList(__(V1, V2))) → isNeList#(V1) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U42(X)) → mark#(X) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | mark#(isNePal(X)) → active#(isNePal(X)) |
| active#(isNeList(V)) → mark#(U31(isQid(V))) | mark#(U51(X1, X2)) → mark#(X1) |
| mark#(isList(X)) → isList#(X) | active#(U11(tt)) → mark#(tt) |
| mark#(U52(X)) → active#(U52(mark(X))) | mark#(u) → active#(u) |
| active#(isList(nil)) → mark#(tt) | active#(U61(tt)) → mark#(tt) |
| mark#(nil) → active#(nil) | mark#(U61(X)) → active#(U61(mark(X))) |
| mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) | mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) → mark#(X1) | mark#(U11(X)) → active#(U11(mark(X))) |
| mark#(U61(X)) → mark#(X) | active#(isQid(o)) → mark#(tt) |
| active#(U72(tt)) → mark#(tt) | U61#(mark(X)) → U61#(X) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isNePal(__(I, __(P, I)))) → isQid#(I) | active#(isQid(u)) → mark#(tt) |
| mark#(isList(X)) → active#(isList(X)) | active#(U51(tt, V2)) → isList#(V2) |
| mark#(U22(X)) → mark#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
Problem 2: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| active#(isNeList(__(V1, V2))) | → | mark#(U41(isList(V1), V2)) | | active#(isQid(a)) | → | mark#(tt) |
| active#(U51(tt, V2)) | → | mark#(U52(isList(V2))) | | active#(isList(__(V1, V2))) | → | isList#(V1) |
| active#(__(__(X, Y), Z)) | → | mark#(__(X, __(Y, Z))) | | active#(__(X, nil)) | → | mark#(X) |
| mark#(U61(X)) | → | U61#(mark(X)) | | mark#(a) | → | active#(a) |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | | active#(U71(tt, P)) | → | U72#(isPal(P)) |
| active#(U21(tt, V2)) | → | mark#(U22(isList(V2))) | | mark#(e) | → | active#(e) |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | | active#(U22(tt)) | → | mark#(tt) |
| mark#(i) | → | active#(i) | | active#(U71(tt, P)) | → | mark#(U72(isPal(P))) |
| mark#(U81(X)) | → | mark#(X) | | active#(isQid(i)) | → | mark#(tt) |
| mark#(__(X1, X2)) | → | mark#(X2) | | mark#(U72(X)) | → | active#(U72(mark(X))) |
| mark#(U72(X)) | → | mark#(X) | | active#(isQid(e)) | → | mark#(tt) |
| mark#(U81(X)) | → | active#(U81(mark(X))) | | active#(U41(tt, V2)) | → | isNeList#(V2) |
| active#(U81(tt)) | → | mark#(tt) | | mark#(isPal(X)) | → | active#(isPal(X)) |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | | mark#(__(X1, X2)) | → | active#(__(mark(X1), mark(X2))) |
| mark#(U52(X)) | → | mark#(X) | | mark#(U71(X1, X2)) | → | mark#(X1) |
| mark#(isQid(X)) | → | active#(isQid(X)) | | active#(U31(tt)) | → | mark#(tt) |
| mark#(U42(X)) | → | active#(U42(mark(X))) | | mark#(isNeList(X)) | → | active#(isNeList(X)) |
| active#(isNePal(V)) | → | U61#(isQid(V)) | | active#(isNePal(V)) | → | mark#(U61(isQid(V))) |
| U61#(active(X)) | → | U61#(X) | | mark#(U31(X)) | → | mark#(X) |
| active#(isPal(nil)) | → | mark#(tt) | | mark#(__(X1, X2)) | → | mark#(X1) |
| active#(U52(tt)) | → | mark#(tt) | | active#(isList(V)) | → | mark#(U11(isNeList(V))) |
| mark#(U22(X)) | → | active#(U22(mark(X))) | | active#(U42(tt)) | → | mark#(tt) |
| mark#(isNeList(X)) | → | isNeList#(X) | | active#(isList(__(V1, V2))) | → | mark#(U21(isList(V1), V2)) |
| active#(isNeList(__(V1, V2))) | → | isNeList#(V1) | | active#(U41(tt, V2)) | → | mark#(U42(isNeList(V2))) |
| mark#(tt) | → | active#(tt) | | mark#(o) | → | active#(o) |
| mark#(U11(X)) | → | mark#(X) | | mark#(U21(X1, X2)) | → | mark#(X1) |
| mark#(U42(X)) | → | mark#(X) | | active#(isNePal(__(I, __(P, I)))) | → | mark#(U71(isQid(I), P)) |
| active#(isNeList(V)) | → | mark#(U31(isQid(V))) | | mark#(isNePal(X)) | → | active#(isNePal(X)) |
| mark#(U51(X1, X2)) | → | mark#(X1) | | active#(U11(tt)) | → | mark#(tt) |
| mark#(u) | → | active#(u) | | mark#(U52(X)) | → | active#(U52(mark(X))) |
| active#(isList(nil)) | → | mark#(tt) | | active#(U61(tt)) | → | mark#(tt) |
| mark#(nil) | → | active#(nil) | | mark#(U61(X)) | → | active#(U61(mark(X))) |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | | mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) |
| mark#(U41(X1, X2)) | → | mark#(X1) | | mark#(U11(X)) | → | active#(U11(mark(X))) |
| mark#(U61(X)) | → | mark#(X) | | active#(isQid(o)) | → | mark#(tt) |
| active#(U72(tt)) | → | mark#(tt) | | U61#(mark(X)) | → | U61#(X) |
| active#(isList(V)) | → | U11#(isNeList(V)) | | active#(__(nil, X)) | → | mark#(X) |
| mark#(U31(X)) | → | active#(U31(mark(X))) | | active#(isQid(u)) | → | mark#(tt) |
| mark#(isList(X)) | → | active#(isList(X)) | | mark#(U22(X)) | → | mark#(X) |
| active#(isPal(V)) | → | mark#(U81(isNePal(V))) | | active#(isNeList(__(V1, V2))) | → | mark#(U51(isNeList(V1), V2)) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
The following SCCs where found
| active#(isNeList(__(V1, V2))) → mark#(U41(isList(V1), V2)) | active#(U51(tt, V2)) → mark#(U52(isList(V2))) |
| active#(isQid(a)) → mark#(tt) | active#(__(__(X, Y), Z)) → mark#(__(X, __(Y, Z))) |
| active#(__(X, nil)) → mark#(X) | mark#(a) → active#(a) |
| active#(U21(tt, V2)) → mark#(U22(isList(V2))) | mark#(e) → active#(e) |
| mark#(U41(X1, X2)) → active#(U41(mark(X1), X2)) | active#(U22(tt)) → mark#(tt) |
| mark#(i) → active#(i) | mark#(U81(X)) → mark#(X) |
| active#(U71(tt, P)) → mark#(U72(isPal(P))) | active#(isQid(i)) → mark#(tt) |
| mark#(U72(X)) → active#(U72(mark(X))) | mark#(__(X1, X2)) → mark#(X2) |
| mark#(U72(X)) → mark#(X) | active#(isQid(e)) → mark#(tt) |
| mark#(U81(X)) → active#(U81(mark(X))) | active#(U81(tt)) → mark#(tt) |
| mark#(isPal(X)) → active#(isPal(X)) | mark#(U51(X1, X2)) → active#(U51(mark(X1), X2)) |
| mark#(__(X1, X2)) → active#(__(mark(X1), mark(X2))) | mark#(U52(X)) → mark#(X) |
| mark#(isQid(X)) → active#(isQid(X)) | mark#(U71(X1, X2)) → mark#(X1) |
| active#(U31(tt)) → mark#(tt) | mark#(U42(X)) → active#(U42(mark(X))) |
| mark#(isNeList(X)) → active#(isNeList(X)) | active#(isNePal(V)) → mark#(U61(isQid(V))) |
| mark#(U31(X)) → mark#(X) | active#(isPal(nil)) → mark#(tt) |
| mark#(__(X1, X2)) → mark#(X1) | active#(isList(V)) → mark#(U11(isNeList(V))) |
| mark#(U22(X)) → active#(U22(mark(X))) | active#(U52(tt)) → mark#(tt) |
| active#(U42(tt)) → mark#(tt) | active#(isList(__(V1, V2))) → mark#(U21(isList(V1), V2)) |
| active#(U41(tt, V2)) → mark#(U42(isNeList(V2))) | mark#(tt) → active#(tt) |
| mark#(o) → active#(o) | mark#(U11(X)) → mark#(X) |
| mark#(U42(X)) → mark#(X) | mark#(U21(X1, X2)) → mark#(X1) |
| active#(isNePal(__(I, __(P, I)))) → mark#(U71(isQid(I), P)) | active#(isNeList(V)) → mark#(U31(isQid(V))) |
| mark#(isNePal(X)) → active#(isNePal(X)) | mark#(U51(X1, X2)) → mark#(X1) |
| active#(U11(tt)) → mark#(tt) | mark#(u) → active#(u) |
| mark#(U52(X)) → active#(U52(mark(X))) | active#(U61(tt)) → mark#(tt) |
| active#(isList(nil)) → mark#(tt) | mark#(nil) → active#(nil) |
| mark#(U61(X)) → active#(U61(mark(X))) | mark#(U21(X1, X2)) → active#(U21(mark(X1), X2)) |
| mark#(U71(X1, X2)) → active#(U71(mark(X1), X2)) | mark#(U41(X1, X2)) → mark#(X1) |
| mark#(U11(X)) → active#(U11(mark(X))) | mark#(U61(X)) → mark#(X) |
| active#(isQid(o)) → mark#(tt) | active#(U72(tt)) → mark#(tt) |
| active#(__(nil, X)) → mark#(X) | mark#(U31(X)) → active#(U31(mark(X))) |
| active#(isQid(u)) → mark#(tt) | mark#(isList(X)) → active#(isList(X)) |
| mark#(U22(X)) → mark#(X) | active#(isNeList(__(V1, V2))) → mark#(U51(isNeList(V1), V2)) |
| active#(isPal(V)) → mark#(U81(isNePal(V))) |
| U61#(mark(X)) → U61#(X) | U61#(active(X)) → U61#(X) |
Problem 4: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| U72#(mark(X)) | → | U72#(X) | | U72#(active(X)) | → | U72#(X) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| U72#(mark(X)) | → | U72#(X) | | U72#(active(X)) | → | U72#(X) |
Problem 9: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| __#(active(X1), X2) | → | __#(X1, X2) | | __#(mark(X1), X2) | → | __#(X1, X2) |
| __#(X1, mark(X2)) | → | __#(X1, X2) | | __#(X1, active(X2)) | → | __#(X1, X2) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| __#(mark(X1), X2) | → | __#(X1, X2) | | __#(active(X1), X2) | → | __#(X1, X2) |
Problem 11: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| U41#(X1, mark(X2)) | → | U41#(X1, X2) | | U41#(X1, active(X2)) | → | U41#(X1, X2) |
| U41#(mark(X1), X2) | → | U41#(X1, X2) | | U41#(active(X1), X2) | → | U41#(X1, X2) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| U41#(mark(X1), X2) | → | U41#(X1, X2) | | U41#(active(X1), X2) | → | U41#(X1, X2) |
Problem 17: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| U61#(mark(X)) | → | U61#(X) | | U61#(active(X)) | → | U61#(X) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| U61#(mark(X)) | → | U61#(X) | | U61#(active(X)) | → | U61#(X) |
Problem 20: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| U21#(X1, mark(X2)) | → | U21#(X1, X2) | | U21#(mark(X1), X2) | → | U21#(X1, X2) |
| U21#(active(X1), X2) | → | U21#(X1, X2) | | U21#(X1, active(X2)) | → | U21#(X1, X2) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| U21#(mark(X1), X2) | → | U21#(X1, X2) | | U21#(active(X1), X2) | → | U21#(X1, X2) |
Problem 21: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| U31#(active(X)) | → | U31#(X) | | U31#(mark(X)) | → | U31#(X) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| U31#(active(X)) | → | U31#(X) | | U31#(mark(X)) | → | U31#(X) |
Problem 25: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| U51#(X1, mark(X2)) | → | U51#(X1, X2) | | U51#(mark(X1), X2) | → | U51#(X1, X2) |
| U51#(X1, active(X2)) | → | U51#(X1, X2) | | U51#(active(X1), X2) | → | U51#(X1, X2) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| U51#(mark(X1), X2) | → | U51#(X1, X2) | | U51#(active(X1), X2) | → | U51#(X1, X2) |
Problem 33: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| U11#(active(X)) | → | U11#(X) | | U11#(mark(X)) | → | U11#(X) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| U11#(active(X)) | → | U11#(X) | | U11#(mark(X)) | → | U11#(X) |
Problem 38: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| U52#(active(X)) | → | U52#(X) | | U52#(mark(X)) | → | U52#(X) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| U52#(active(X)) | → | U52#(X) | | U52#(mark(X)) | → | U52#(X) |
Problem 39: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| isNePal#(active(X)) | → | isNePal#(X) | | isNePal#(mark(X)) | → | isNePal#(X) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| isNePal#(active(X)) | → | isNePal#(X) | | isNePal#(mark(X)) | → | isNePal#(X) |
Problem 41: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| isNeList#(active(X)) | → | isNeList#(X) | | isNeList#(mark(X)) | → | isNeList#(X) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| isNeList#(active(X)) | → | isNeList#(X) | | isNeList#(mark(X)) | → | isNeList#(X) |
Problem 43: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| U71#(X1, active(X2)) | → | U71#(X1, X2) | | U71#(active(X1), X2) | → | U71#(X1, X2) |
| U71#(mark(X1), X2) | → | U71#(X1, X2) | | U71#(X1, mark(X2)) | → | U71#(X1, X2) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| U71#(active(X1), X2) | → | U71#(X1, X2) | | U71#(mark(X1), X2) | → | U71#(X1, X2) |
Problem 49: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| U81#(mark(X)) | → | U81#(X) | | U81#(active(X)) | → | U81#(X) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| U81#(mark(X)) | → | U81#(X) | | U81#(active(X)) | → | U81#(X) |
Problem 51: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| isQid#(mark(X)) | → | isQid#(X) | | isQid#(active(X)) | → | isQid#(X) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| isQid#(mark(X)) | → | isQid#(X) | | isQid#(active(X)) | → | isQid#(X) |
Problem 53: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| isPal#(mark(X)) | → | isPal#(X) | | isPal#(active(X)) | → | isPal#(X) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| isPal#(mark(X)) | → | isPal#(X) | | isPal#(active(X)) | → | isPal#(X) |
Problem 57: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| U42#(mark(X)) | → | U42#(X) | | U42#(active(X)) | → | U42#(X) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| U42#(mark(X)) | → | U42#(X) | | U42#(active(X)) | → | U42#(X) |
Problem 62: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| U22#(mark(X)) | → | U22#(X) | | U22#(active(X)) | → | U22#(X) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| U22#(mark(X)) | → | U22#(X) | | U22#(active(X)) | → | U22#(X) |
Problem 64: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| isList#(active(X)) | → | isList#(X) | | isList#(mark(X)) | → | isList#(X) |
Rewrite Rules
| active(__(__(X, Y), Z)) | → | mark(__(X, __(Y, Z))) | | active(__(X, nil)) | → | mark(X) |
| active(__(nil, X)) | → | mark(X) | | active(U11(tt)) | → | mark(tt) |
| active(U21(tt, V2)) | → | mark(U22(isList(V2))) | | active(U22(tt)) | → | mark(tt) |
| active(U31(tt)) | → | mark(tt) | | active(U41(tt, V2)) | → | mark(U42(isNeList(V2))) |
| active(U42(tt)) | → | mark(tt) | | active(U51(tt, V2)) | → | mark(U52(isList(V2))) |
| active(U52(tt)) | → | mark(tt) | | active(U61(tt)) | → | mark(tt) |
| active(U71(tt, P)) | → | mark(U72(isPal(P))) | | active(U72(tt)) | → | mark(tt) |
| active(U81(tt)) | → | mark(tt) | | active(isList(V)) | → | mark(U11(isNeList(V))) |
| active(isList(nil)) | → | mark(tt) | | active(isList(__(V1, V2))) | → | mark(U21(isList(V1), V2)) |
| active(isNeList(V)) | → | mark(U31(isQid(V))) | | active(isNeList(__(V1, V2))) | → | mark(U41(isList(V1), V2)) |
| active(isNeList(__(V1, V2))) | → | mark(U51(isNeList(V1), V2)) | | active(isNePal(V)) | → | mark(U61(isQid(V))) |
| active(isNePal(__(I, __(P, I)))) | → | mark(U71(isQid(I), P)) | | active(isPal(V)) | → | mark(U81(isNePal(V))) |
| active(isPal(nil)) | → | mark(tt) | | active(isQid(a)) | → | mark(tt) |
| active(isQid(e)) | → | mark(tt) | | active(isQid(i)) | → | mark(tt) |
| active(isQid(o)) | → | mark(tt) | | active(isQid(u)) | → | mark(tt) |
| mark(__(X1, X2)) | → | active(__(mark(X1), mark(X2))) | | mark(nil) | → | active(nil) |
| mark(U11(X)) | → | active(U11(mark(X))) | | mark(tt) | → | active(tt) |
| mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | | mark(U22(X)) | → | active(U22(mark(X))) |
| mark(isList(X)) | → | active(isList(X)) | | mark(U31(X)) | → | active(U31(mark(X))) |
| mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | | mark(U42(X)) | → | active(U42(mark(X))) |
| mark(isNeList(X)) | → | active(isNeList(X)) | | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) |
| mark(U52(X)) | → | active(U52(mark(X))) | | mark(U61(X)) | → | active(U61(mark(X))) |
| mark(U71(X1, X2)) | → | active(U71(mark(X1), X2)) | | mark(U72(X)) | → | active(U72(mark(X))) |
| mark(isPal(X)) | → | active(isPal(X)) | | mark(U81(X)) | → | active(U81(mark(X))) |
| mark(isQid(X)) | → | active(isQid(X)) | | mark(isNePal(X)) | → | active(isNePal(X)) |
| mark(a) | → | active(a) | | mark(e) | → | active(e) |
| mark(i) | → | active(i) | | mark(o) | → | active(o) |
| mark(u) | → | active(u) | | __(mark(X1), X2) | → | __(X1, X2) |
| __(X1, mark(X2)) | → | __(X1, X2) | | __(active(X1), X2) | → | __(X1, X2) |
| __(X1, active(X2)) | → | __(X1, X2) | | U11(mark(X)) | → | U11(X) |
| U11(active(X)) | → | U11(X) | | U21(mark(X1), X2) | → | U21(X1, X2) |
| U21(X1, mark(X2)) | → | U21(X1, X2) | | U21(active(X1), X2) | → | U21(X1, X2) |
| U21(X1, active(X2)) | → | U21(X1, X2) | | U22(mark(X)) | → | U22(X) |
| U22(active(X)) | → | U22(X) | | isList(mark(X)) | → | isList(X) |
| isList(active(X)) | → | isList(X) | | U31(mark(X)) | → | U31(X) |
| U31(active(X)) | → | U31(X) | | U41(mark(X1), X2) | → | U41(X1, X2) |
| U41(X1, mark(X2)) | → | U41(X1, X2) | | U41(active(X1), X2) | → | U41(X1, X2) |
| U41(X1, active(X2)) | → | U41(X1, X2) | | U42(mark(X)) | → | U42(X) |
| U42(active(X)) | → | U42(X) | | isNeList(mark(X)) | → | isNeList(X) |
| isNeList(active(X)) | → | isNeList(X) | | U51(mark(X1), X2) | → | U51(X1, X2) |
| U51(X1, mark(X2)) | → | U51(X1, X2) | | U51(active(X1), X2) | → | U51(X1, X2) |
| U51(X1, active(X2)) | → | U51(X1, X2) | | U52(mark(X)) | → | U52(X) |
| U52(active(X)) | → | U52(X) | | U61(mark(X)) | → | U61(X) |
| U61(active(X)) | → | U61(X) | | U71(mark(X1), X2) | → | U71(X1, X2) |
| U71(X1, mark(X2)) | → | U71(X1, X2) | | U71(active(X1), X2) | → | U71(X1, X2) |
| U71(X1, active(X2)) | → | U71(X1, X2) | | U72(mark(X)) | → | U72(X) |
| U72(active(X)) | → | U72(X) | | isPal(mark(X)) | → | isPal(X) |
| isPal(active(X)) | → | isPal(X) | | U81(mark(X)) | → | U81(X) |
| U81(active(X)) | → | U81(X) | | isQid(mark(X)) | → | isQid(X) |
| isQid(active(X)) | → | isQid(X) | | isNePal(mark(X)) | → | isNePal(X) |
| isNePal(active(X)) | → | isNePal(X) |
Original Signature
Termination of terms over the following signature is verified: isList, isNeList, __, U61, U42, U41, isNePal, U21, U22, e, a, o, mark, isPal, U71, i, U72, u, U51, tt, U52, U81, U11, active, isQid, U31, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| isList#(active(X)) | → | isList#(X) | | isList#(mark(X)) | → | isList#(X) |