MAYBE

The TRS could not be proven terminating. The proof attempt took 803 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (0ms).
 | – Problem 2 was processed with processor SubtermCriterion (0ms).
 | – Problem 3 remains open; application of the following processors failed [SubtermCriterion (1ms), DependencyGraph (2ms), PolynomialLinearRange4iUR (93ms), DependencyGraph (1ms), PolynomialLinearRange8NegiUR (159ms), DependencyGraph (1ms), ReductionPairSAT (446ms), DependencyGraph (1ms), SizeChangePrinciple (7ms)].

The following open problems remain:



Open Dependency Pair Problem 3

Dependency Pairs

f#(g(x), x, y)f#(y, y, g(y))

Rewrite Rules

f(g(x), x, y)f(y, y, g(y))g(g(x))g(x)

Original Signature

Termination of terms over the following signature is verified: f, g


Problem 1: DependencyGraph



Dependency Pair Problem

Dependency Pairs

f#(g(x), x, y)f#(y, y, g(y))g#(g(x))g#(x)
f#(g(x), x, y)g#(y)

Rewrite Rules

f(g(x), x, y)f(y, y, g(y))g(g(x))g(x)

Original Signature

Termination of terms over the following signature is verified: f, g

Strategy


The following SCCs where found

f#(g(x), x, y) → f#(y, y, g(y))

g#(g(x)) → g#(x)

Problem 2: SubtermCriterion



Dependency Pair Problem

Dependency Pairs

g#(g(x))g#(x)

Rewrite Rules

f(g(x), x, y)f(y, y, g(y))g(g(x))g(x)

Original Signature

Termination of terms over the following signature is verified: f, g

Strategy


Projection

The following projection was used:

Thus, the following dependency pairs are removed:

g#(g(x))g#(x)