TIMEOUT
The TRS could not be proven terminating. The proof attempt took 60001 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (1199ms).
| – Problem 2 was processed with processor SubtermCriterion (1ms).
| – Problem 3 was processed with processor SubtermCriterion (1ms).
| – Problem 4 remains open; application of the following processors failed [SubtermCriterion (1ms), DependencyGraph (89ms), PolynomialLinearRange4iUR (1971ms), DependencyGraph (84ms), PolynomialLinearRange8NegiUR (10001ms), DependencyGraph (59ms), ReductionPairSAT (2593ms), DependencyGraph (62ms), SizeChangePrinciple (timeout)].
| – Problem 5 was processed with processor SubtermCriterion (1ms).
| – Problem 6 remains open; application of the following processors failed [SubtermCriterion (0ms), DependencyGraph (40ms), PolynomialLinearRange4iUR (385ms), DependencyGraph (2ms), PolynomialLinearRange8NegiUR (2ms), DependencyGraph (1ms), ReductionPairSAT (941ms), DependencyGraph (1ms)].
| – Problem 7 remains open; application of the following processors failed [SubtermCriterion (0ms), DependencyGraph (10ms), PolynomialLinearRange4iUR (1291ms), DependencyGraph (7ms), PolynomialLinearRange8NegiUR (29ms), DependencyGraph (7ms), ReductionPairSAT (1581ms), DependencyGraph (8ms)].
The following open problems remain:
Open Dependency Pair Problem 4
Dependency Pairs
| activate#(n__sel(X1, X2)) | → | sel#(activate(X1), activate(X2)) | | activate#(n__sel(X1, X2)) | → | activate#(X2) |
| activate#(n__s(X)) | → | activate#(X) | | activate#(n__sel(X1, X2)) | → | activate#(X1) |
| activate#(n__from(X)) | → | activate#(X) | | sel#(s(X), cons(Y, Z)) | → | sel#(X, activate(Z)) |
| activate#(n__first(X1, X2)) | → | activate#(X2) | | activate#(n__first(X1, X2)) | → | first#(activate(X1), activate(X2)) |
| activate#(n__first(X1, X2)) | → | activate#(X1) | | activate#(n__cons(X1, X2)) | → | activate#(X1) |
| sel#(s(X), cons(Y, Z)) | → | activate#(Z) | | first#(s(X), cons(Y, Z)) | → | activate#(Z) |
Rewrite Rules
| sel(s(X), cons(Y, Z)) | → | sel(X, activate(Z)) | | sel(0, cons(X, Z)) | → | X |
| first(0, Z) | → | nil | | first(s(X), cons(Y, Z)) | → | cons(Y, n__first(X, activate(Z))) |
| from(X) | → | cons(X, n__from(n__s(X))) | | sel1(s(X), cons(Y, Z)) | → | sel1(X, activate(Z)) |
| sel1(0, cons(X, Z)) | → | quote(X) | | first1(0, Z) | → | nil1 |
| first1(s(X), cons(Y, Z)) | → | cons1(quote(Y), first1(X, activate(Z))) | | quote(n__0) | → | 01 |
| quote1(n__cons(X, Z)) | → | cons1(quote(activate(X)), quote1(activate(Z))) | | quote1(n__nil) | → | nil1 |
| quote(n__s(X)) | → | s1(quote(activate(X))) | | quote(n__sel(X, Z)) | → | sel1(activate(X), activate(Z)) |
| quote1(n__first(X, Z)) | → | first1(activate(X), activate(Z)) | | unquote(01) | → | 0 |
| unquote(s1(X)) | → | s(unquote(X)) | | unquote1(nil1) | → | nil |
| unquote1(cons1(X, Z)) | → | fcons(unquote(X), unquote1(Z)) | | fcons(X, Z) | → | cons(X, Z) |
| first(X1, X2) | → | n__first(X1, X2) | | from(X) | → | n__from(X) |
| s(X) | → | n__s(X) | | 0 | → | n__0 |
| cons(X1, X2) | → | n__cons(X1, X2) | | nil | → | n__nil |
| sel(X1, X2) | → | n__sel(X1, X2) | | activate(n__first(X1, X2)) | → | first(activate(X1), activate(X2)) |
| activate(n__from(X)) | → | from(activate(X)) | | activate(n__s(X)) | → | s(activate(X)) |
| activate(n__0) | → | 0 | | activate(n__cons(X1, X2)) | → | cons(activate(X1), X2) |
| activate(n__nil) | → | nil | | activate(n__sel(X1, X2)) | → | sel(activate(X1), activate(X2)) |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: cons1, n__from, from, n__sel, n__s, activate, n__0, unquote, sel1, n__first, unquote1, quote, n__nil, cons, s1, fcons, 01, first1, n__cons, quote1, 0, s, nil1, first, sel, nil
Open Dependency Pair Problem 6
Dependency Pairs
| quote1#(n__cons(X, Z)) | → | quote1#(activate(Z)) |
Rewrite Rules
| sel(s(X), cons(Y, Z)) | → | sel(X, activate(Z)) | | sel(0, cons(X, Z)) | → | X |
| first(0, Z) | → | nil | | first(s(X), cons(Y, Z)) | → | cons(Y, n__first(X, activate(Z))) |
| from(X) | → | cons(X, n__from(n__s(X))) | | sel1(s(X), cons(Y, Z)) | → | sel1(X, activate(Z)) |
| sel1(0, cons(X, Z)) | → | quote(X) | | first1(0, Z) | → | nil1 |
| first1(s(X), cons(Y, Z)) | → | cons1(quote(Y), first1(X, activate(Z))) | | quote(n__0) | → | 01 |
| quote1(n__cons(X, Z)) | → | cons1(quote(activate(X)), quote1(activate(Z))) | | quote1(n__nil) | → | nil1 |
| quote(n__s(X)) | → | s1(quote(activate(X))) | | quote(n__sel(X, Z)) | → | sel1(activate(X), activate(Z)) |
| quote1(n__first(X, Z)) | → | first1(activate(X), activate(Z)) | | unquote(01) | → | 0 |
| unquote(s1(X)) | → | s(unquote(X)) | | unquote1(nil1) | → | nil |
| unquote1(cons1(X, Z)) | → | fcons(unquote(X), unquote1(Z)) | | fcons(X, Z) | → | cons(X, Z) |
| first(X1, X2) | → | n__first(X1, X2) | | from(X) | → | n__from(X) |
| s(X) | → | n__s(X) | | 0 | → | n__0 |
| cons(X1, X2) | → | n__cons(X1, X2) | | nil | → | n__nil |
| sel(X1, X2) | → | n__sel(X1, X2) | | activate(n__first(X1, X2)) | → | first(activate(X1), activate(X2)) |
| activate(n__from(X)) | → | from(activate(X)) | | activate(n__s(X)) | → | s(activate(X)) |
| activate(n__0) | → | 0 | | activate(n__cons(X1, X2)) | → | cons(activate(X1), X2) |
| activate(n__nil) | → | nil | | activate(n__sel(X1, X2)) | → | sel(activate(X1), activate(X2)) |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: cons1, n__from, from, n__sel, n__s, activate, n__0, unquote, sel1, n__first, unquote1, quote, n__nil, cons, s1, fcons, 01, first1, n__cons, quote1, 0, s, nil1, first, sel, nil
Open Dependency Pair Problem 7
Dependency Pairs
| sel1#(s(X), cons(Y, Z)) | → | sel1#(X, activate(Z)) | | quote#(n__s(X)) | → | quote#(activate(X)) |
| quote#(n__sel(X, Z)) | → | sel1#(activate(X), activate(Z)) | | sel1#(0, cons(X, Z)) | → | quote#(X) |
Rewrite Rules
| sel(s(X), cons(Y, Z)) | → | sel(X, activate(Z)) | | sel(0, cons(X, Z)) | → | X |
| first(0, Z) | → | nil | | first(s(X), cons(Y, Z)) | → | cons(Y, n__first(X, activate(Z))) |
| from(X) | → | cons(X, n__from(n__s(X))) | | sel1(s(X), cons(Y, Z)) | → | sel1(X, activate(Z)) |
| sel1(0, cons(X, Z)) | → | quote(X) | | first1(0, Z) | → | nil1 |
| first1(s(X), cons(Y, Z)) | → | cons1(quote(Y), first1(X, activate(Z))) | | quote(n__0) | → | 01 |
| quote1(n__cons(X, Z)) | → | cons1(quote(activate(X)), quote1(activate(Z))) | | quote1(n__nil) | → | nil1 |
| quote(n__s(X)) | → | s1(quote(activate(X))) | | quote(n__sel(X, Z)) | → | sel1(activate(X), activate(Z)) |
| quote1(n__first(X, Z)) | → | first1(activate(X), activate(Z)) | | unquote(01) | → | 0 |
| unquote(s1(X)) | → | s(unquote(X)) | | unquote1(nil1) | → | nil |
| unquote1(cons1(X, Z)) | → | fcons(unquote(X), unquote1(Z)) | | fcons(X, Z) | → | cons(X, Z) |
| first(X1, X2) | → | n__first(X1, X2) | | from(X) | → | n__from(X) |
| s(X) | → | n__s(X) | | 0 | → | n__0 |
| cons(X1, X2) | → | n__cons(X1, X2) | | nil | → | n__nil |
| sel(X1, X2) | → | n__sel(X1, X2) | | activate(n__first(X1, X2)) | → | first(activate(X1), activate(X2)) |
| activate(n__from(X)) | → | from(activate(X)) | | activate(n__s(X)) | → | s(activate(X)) |
| activate(n__0) | → | 0 | | activate(n__cons(X1, X2)) | → | cons(activate(X1), X2) |
| activate(n__nil) | → | nil | | activate(n__sel(X1, X2)) | → | sel(activate(X1), activate(X2)) |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: cons1, n__from, from, n__sel, n__s, activate, n__0, unquote, sel1, n__first, unquote1, quote, n__nil, cons, s1, fcons, 01, first1, n__cons, quote1, 0, s, nil1, first, sel, nil
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| quote#(n__sel(X, Z)) | → | activate#(X) | | activate#(n__sel(X1, X2)) | → | activate#(X2) |
| quote1#(n__first(X, Z)) | → | activate#(Z) | | activate#(n__s(X)) | → | activate#(X) |
| quote1#(n__cons(X, Z)) | → | quote#(activate(X)) | | activate#(n__sel(X1, X2)) | → | activate#(X1) |
| sel#(s(X), cons(Y, Z)) | → | sel#(X, activate(Z)) | | activate#(n__first(X1, X2)) | → | activate#(X2) |
| quote1#(n__first(X, Z)) | → | activate#(X) | | unquote1#(cons1(X, Z)) | → | fcons#(unquote(X), unquote1(Z)) |
| activate#(n__first(X1, X2)) | → | first#(activate(X1), activate(X2)) | | activate#(n__first(X1, X2)) | → | activate#(X1) |
| activate#(n__cons(X1, X2)) | → | cons#(activate(X1), X2) | | activate#(n__cons(X1, X2)) | → | activate#(X1) |
| unquote1#(cons1(X, Z)) | → | unquote1#(Z) | | first#(s(X), cons(Y, Z)) | → | activate#(Z) |
| sel#(s(X), cons(Y, Z)) | → | activate#(Z) | | quote#(n__sel(X, Z)) | → | sel1#(activate(X), activate(Z)) |
| first#(0, Z) | → | nil# | | quote1#(n__cons(X, Z)) | → | activate#(X) |
| first1#(s(X), cons(Y, Z)) | → | first1#(X, activate(Z)) | | first1#(s(X), cons(Y, Z)) | → | activate#(Z) |
| sel1#(0, cons(X, Z)) | → | quote#(X) | | fcons#(X, Z) | → | cons#(X, Z) |
| quote1#(n__cons(X, Z)) | → | activate#(Z) | | activate#(n__sel(X1, X2)) | → | sel#(activate(X1), activate(X2)) |
| sel1#(s(X), cons(Y, Z)) | → | activate#(Z) | | unquote#(s1(X)) | → | unquote#(X) |
| first1#(s(X), cons(Y, Z)) | → | quote#(Y) | | quote#(n__s(X)) | → | activate#(X) |
| activate#(n__from(X)) | → | activate#(X) | | unquote1#(nil1) | → | nil# |
| quote1#(n__first(X, Z)) | → | first1#(activate(X), activate(Z)) | | unquote1#(cons1(X, Z)) | → | unquote#(X) |
| unquote#(01) | → | 0# | | unquote#(s1(X)) | → | s#(unquote(X)) |
| quote#(n__sel(X, Z)) | → | activate#(Z) | | sel1#(s(X), cons(Y, Z)) | → | sel1#(X, activate(Z)) |
| activate#(n__nil) | → | nil# | | quote#(n__s(X)) | → | quote#(activate(X)) |
| from#(X) | → | cons#(X, n__from(n__s(X))) | | first#(s(X), cons(Y, Z)) | → | cons#(Y, n__first(X, activate(Z))) |
| activate#(n__from(X)) | → | from#(activate(X)) | | activate#(n__0) | → | 0# |
| activate#(n__s(X)) | → | s#(activate(X)) | | quote1#(n__cons(X, Z)) | → | quote1#(activate(Z)) |
Rewrite Rules
| sel(s(X), cons(Y, Z)) | → | sel(X, activate(Z)) | | sel(0, cons(X, Z)) | → | X |
| first(0, Z) | → | nil | | first(s(X), cons(Y, Z)) | → | cons(Y, n__first(X, activate(Z))) |
| from(X) | → | cons(X, n__from(n__s(X))) | | sel1(s(X), cons(Y, Z)) | → | sel1(X, activate(Z)) |
| sel1(0, cons(X, Z)) | → | quote(X) | | first1(0, Z) | → | nil1 |
| first1(s(X), cons(Y, Z)) | → | cons1(quote(Y), first1(X, activate(Z))) | | quote(n__0) | → | 01 |
| quote1(n__cons(X, Z)) | → | cons1(quote(activate(X)), quote1(activate(Z))) | | quote1(n__nil) | → | nil1 |
| quote(n__s(X)) | → | s1(quote(activate(X))) | | quote(n__sel(X, Z)) | → | sel1(activate(X), activate(Z)) |
| quote1(n__first(X, Z)) | → | first1(activate(X), activate(Z)) | | unquote(01) | → | 0 |
| unquote(s1(X)) | → | s(unquote(X)) | | unquote1(nil1) | → | nil |
| unquote1(cons1(X, Z)) | → | fcons(unquote(X), unquote1(Z)) | | fcons(X, Z) | → | cons(X, Z) |
| first(X1, X2) | → | n__first(X1, X2) | | from(X) | → | n__from(X) |
| s(X) | → | n__s(X) | | 0 | → | n__0 |
| cons(X1, X2) | → | n__cons(X1, X2) | | nil | → | n__nil |
| sel(X1, X2) | → | n__sel(X1, X2) | | activate(n__first(X1, X2)) | → | first(activate(X1), activate(X2)) |
| activate(n__from(X)) | → | from(activate(X)) | | activate(n__s(X)) | → | s(activate(X)) |
| activate(n__0) | → | 0 | | activate(n__cons(X1, X2)) | → | cons(activate(X1), X2) |
| activate(n__nil) | → | nil | | activate(n__sel(X1, X2)) | → | sel(activate(X1), activate(X2)) |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: cons1, n__from, from, n__sel, activate, n__s, unquote, n__0, sel1, unquote1, n__first, quote, n__nil, cons, s1, fcons, 01, first1, n__cons, quote1, 0, s, nil1, first, sel, nil
Strategy
The following SCCs where found
| unquote1#(cons1(X, Z)) → unquote1#(Z) |
| unquote#(s1(X)) → unquote#(X) |
| activate#(n__first(X1, X2)) → first#(activate(X1), activate(X2)) | activate#(n__first(X1, X2)) → activate#(X1) |
| activate#(n__cons(X1, X2)) → activate#(X1) | activate#(n__sel(X1, X2)) → sel#(activate(X1), activate(X2)) |
| first#(s(X), cons(Y, Z)) → activate#(Z) | sel#(s(X), cons(Y, Z)) → activate#(Z) |
| activate#(n__sel(X1, X2)) → activate#(X2) | activate#(n__s(X)) → activate#(X) |
| activate#(n__sel(X1, X2)) → activate#(X1) | activate#(n__from(X)) → activate#(X) |
| sel#(s(X), cons(Y, Z)) → sel#(X, activate(Z)) | activate#(n__first(X1, X2)) → activate#(X2) |
| sel1#(s(X), cons(Y, Z)) → sel1#(X, activate(Z)) | quote#(n__s(X)) → quote#(activate(X)) |
| quote#(n__sel(X, Z)) → sel1#(activate(X), activate(Z)) | sel1#(0, cons(X, Z)) → quote#(X) |
| first1#(s(X), cons(Y, Z)) → first1#(X, activate(Z)) |
| quote1#(n__cons(X, Z)) → quote1#(activate(Z)) |
Problem 2: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| unquote#(s1(X)) | → | unquote#(X) |
Rewrite Rules
| sel(s(X), cons(Y, Z)) | → | sel(X, activate(Z)) | | sel(0, cons(X, Z)) | → | X |
| first(0, Z) | → | nil | | first(s(X), cons(Y, Z)) | → | cons(Y, n__first(X, activate(Z))) |
| from(X) | → | cons(X, n__from(n__s(X))) | | sel1(s(X), cons(Y, Z)) | → | sel1(X, activate(Z)) |
| sel1(0, cons(X, Z)) | → | quote(X) | | first1(0, Z) | → | nil1 |
| first1(s(X), cons(Y, Z)) | → | cons1(quote(Y), first1(X, activate(Z))) | | quote(n__0) | → | 01 |
| quote1(n__cons(X, Z)) | → | cons1(quote(activate(X)), quote1(activate(Z))) | | quote1(n__nil) | → | nil1 |
| quote(n__s(X)) | → | s1(quote(activate(X))) | | quote(n__sel(X, Z)) | → | sel1(activate(X), activate(Z)) |
| quote1(n__first(X, Z)) | → | first1(activate(X), activate(Z)) | | unquote(01) | → | 0 |
| unquote(s1(X)) | → | s(unquote(X)) | | unquote1(nil1) | → | nil |
| unquote1(cons1(X, Z)) | → | fcons(unquote(X), unquote1(Z)) | | fcons(X, Z) | → | cons(X, Z) |
| first(X1, X2) | → | n__first(X1, X2) | | from(X) | → | n__from(X) |
| s(X) | → | n__s(X) | | 0 | → | n__0 |
| cons(X1, X2) | → | n__cons(X1, X2) | | nil | → | n__nil |
| sel(X1, X2) | → | n__sel(X1, X2) | | activate(n__first(X1, X2)) | → | first(activate(X1), activate(X2)) |
| activate(n__from(X)) | → | from(activate(X)) | | activate(n__s(X)) | → | s(activate(X)) |
| activate(n__0) | → | 0 | | activate(n__cons(X1, X2)) | → | cons(activate(X1), X2) |
| activate(n__nil) | → | nil | | activate(n__sel(X1, X2)) | → | sel(activate(X1), activate(X2)) |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: cons1, n__from, from, n__sel, activate, n__s, unquote, n__0, sel1, unquote1, n__first, quote, n__nil, cons, s1, fcons, 01, first1, n__cons, quote1, 0, s, nil1, first, sel, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| unquote#(s1(X)) | → | unquote#(X) |
Problem 3: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| unquote1#(cons1(X, Z)) | → | unquote1#(Z) |
Rewrite Rules
| sel(s(X), cons(Y, Z)) | → | sel(X, activate(Z)) | | sel(0, cons(X, Z)) | → | X |
| first(0, Z) | → | nil | | first(s(X), cons(Y, Z)) | → | cons(Y, n__first(X, activate(Z))) |
| from(X) | → | cons(X, n__from(n__s(X))) | | sel1(s(X), cons(Y, Z)) | → | sel1(X, activate(Z)) |
| sel1(0, cons(X, Z)) | → | quote(X) | | first1(0, Z) | → | nil1 |
| first1(s(X), cons(Y, Z)) | → | cons1(quote(Y), first1(X, activate(Z))) | | quote(n__0) | → | 01 |
| quote1(n__cons(X, Z)) | → | cons1(quote(activate(X)), quote1(activate(Z))) | | quote1(n__nil) | → | nil1 |
| quote(n__s(X)) | → | s1(quote(activate(X))) | | quote(n__sel(X, Z)) | → | sel1(activate(X), activate(Z)) |
| quote1(n__first(X, Z)) | → | first1(activate(X), activate(Z)) | | unquote(01) | → | 0 |
| unquote(s1(X)) | → | s(unquote(X)) | | unquote1(nil1) | → | nil |
| unquote1(cons1(X, Z)) | → | fcons(unquote(X), unquote1(Z)) | | fcons(X, Z) | → | cons(X, Z) |
| first(X1, X2) | → | n__first(X1, X2) | | from(X) | → | n__from(X) |
| s(X) | → | n__s(X) | | 0 | → | n__0 |
| cons(X1, X2) | → | n__cons(X1, X2) | | nil | → | n__nil |
| sel(X1, X2) | → | n__sel(X1, X2) | | activate(n__first(X1, X2)) | → | first(activate(X1), activate(X2)) |
| activate(n__from(X)) | → | from(activate(X)) | | activate(n__s(X)) | → | s(activate(X)) |
| activate(n__0) | → | 0 | | activate(n__cons(X1, X2)) | → | cons(activate(X1), X2) |
| activate(n__nil) | → | nil | | activate(n__sel(X1, X2)) | → | sel(activate(X1), activate(X2)) |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: cons1, n__from, from, n__sel, activate, n__s, unquote, n__0, sel1, unquote1, n__first, quote, n__nil, cons, s1, fcons, 01, first1, n__cons, quote1, 0, s, nil1, first, sel, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| unquote1#(cons1(X, Z)) | → | unquote1#(Z) |
Problem 5: SubtermCriterion
Dependency Pair Problem
Dependency Pairs
| first1#(s(X), cons(Y, Z)) | → | first1#(X, activate(Z)) |
Rewrite Rules
| sel(s(X), cons(Y, Z)) | → | sel(X, activate(Z)) | | sel(0, cons(X, Z)) | → | X |
| first(0, Z) | → | nil | | first(s(X), cons(Y, Z)) | → | cons(Y, n__first(X, activate(Z))) |
| from(X) | → | cons(X, n__from(n__s(X))) | | sel1(s(X), cons(Y, Z)) | → | sel1(X, activate(Z)) |
| sel1(0, cons(X, Z)) | → | quote(X) | | first1(0, Z) | → | nil1 |
| first1(s(X), cons(Y, Z)) | → | cons1(quote(Y), first1(X, activate(Z))) | | quote(n__0) | → | 01 |
| quote1(n__cons(X, Z)) | → | cons1(quote(activate(X)), quote1(activate(Z))) | | quote1(n__nil) | → | nil1 |
| quote(n__s(X)) | → | s1(quote(activate(X))) | | quote(n__sel(X, Z)) | → | sel1(activate(X), activate(Z)) |
| quote1(n__first(X, Z)) | → | first1(activate(X), activate(Z)) | | unquote(01) | → | 0 |
| unquote(s1(X)) | → | s(unquote(X)) | | unquote1(nil1) | → | nil |
| unquote1(cons1(X, Z)) | → | fcons(unquote(X), unquote1(Z)) | | fcons(X, Z) | → | cons(X, Z) |
| first(X1, X2) | → | n__first(X1, X2) | | from(X) | → | n__from(X) |
| s(X) | → | n__s(X) | | 0 | → | n__0 |
| cons(X1, X2) | → | n__cons(X1, X2) | | nil | → | n__nil |
| sel(X1, X2) | → | n__sel(X1, X2) | | activate(n__first(X1, X2)) | → | first(activate(X1), activate(X2)) |
| activate(n__from(X)) | → | from(activate(X)) | | activate(n__s(X)) | → | s(activate(X)) |
| activate(n__0) | → | 0 | | activate(n__cons(X1, X2)) | → | cons(activate(X1), X2) |
| activate(n__nil) | → | nil | | activate(n__sel(X1, X2)) | → | sel(activate(X1), activate(X2)) |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: cons1, n__from, from, n__sel, activate, n__s, unquote, n__0, sel1, unquote1, n__first, quote, n__nil, cons, s1, fcons, 01, first1, n__cons, quote1, 0, s, nil1, first, sel, nil
Strategy
Projection
The following projection was used:
Thus, the following dependency pairs are removed:
| first1#(s(X), cons(Y, Z)) | → | first1#(X, activate(Z)) |