TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60000 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (21ms).
 | – Problem 2 remains open; application of the following processors failed [SubtermCriterion (2ms), DependencyGraph (3ms), PolynomialLinearRange4iUR (360ms), DependencyGraph (1ms), PolynomialLinearRange8NegiUR (5008ms), DependencyGraph (1ms), ReductionPairSAT (timeout)].
 | – Problem 3 was processed with processor SubtermCriterion (1ms).

The following open problems remain:



Open Dependency Pair Problem 2

Dependency Pairs

f#(0, 1, g(x, y), z)f#(g(x, y), g(x, y), g(x, y), h(x))

Rewrite Rules

f(0, 1, g(x, y), z)f(g(x, y), g(x, y), g(x, y), h(x))g(0, 1)0
g(0, 1)1h(g(x, y))h(x)

Original Signature

Termination of terms over the following signature is verified: f, g, 1, 0, h


Problem 1: DependencyGraph



Dependency Pair Problem

Dependency Pairs

f#(0, 1, g(x, y), z)h#(x)f#(0, 1, g(x, y), z)g#(x, y)
h#(g(x, y))h#(x)f#(0, 1, g(x, y), z)f#(g(x, y), g(x, y), g(x, y), h(x))

Rewrite Rules

f(0, 1, g(x, y), z)f(g(x, y), g(x, y), g(x, y), h(x))g(0, 1)0
g(0, 1)1h(g(x, y))h(x)

Original Signature

Termination of terms over the following signature is verified: f, g, 1, 0, h

Strategy


The following SCCs where found

h#(g(x, y)) → h#(x)

f#(0, 1, g(x, y), z) → f#(g(x, y), g(x, y), g(x, y), h(x))

Problem 3: SubtermCriterion



Dependency Pair Problem

Dependency Pairs

h#(g(x, y))h#(x)

Rewrite Rules

f(0, 1, g(x, y), z)f(g(x, y), g(x, y), g(x, y), h(x))g(0, 1)0
g(0, 1)1h(g(x, y))h(x)

Original Signature

Termination of terms over the following signature is verified: f, g, 1, 0, h

Strategy


Projection

The following projection was used:

Thus, the following dependency pairs are removed:

h#(g(x, y))h#(x)