MAYBE
The TRS could not be proven terminating. The proof attempt took 34964 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (0ms).
| – Problem 2 remains open; application of the following processors failed [SubtermCriterion (1ms), DependencyGraph (2ms), PolynomialLinearRange4iUR (592ms), DependencyGraph (2ms), PolynomialLinearRange8NegiUR (1765ms), DependencyGraph (1ms), ReductionPairSAT (32227ms), DependencyGraph (4ms), SizeChangePrinciple (153ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| c#(c(z, x, a), a, y) | → | c#(y, a, f(c(z, y, x))) | | c#(c(z, x, a), a, y) | → | c#(z, y, x) |
Rewrite Rules
| b(a, f(b(b(z, y), a))) | → | z | | c(c(z, x, a), a, y) | → | f(f(c(y, a, f(c(z, y, x))))) |
| f(f(c(a, y, z))) | → | b(y, b(z, z)) |
Original Signature
Termination of terms over the following signature is verified: f, b, c, a
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| c#(c(z, x, a), a, y) | → | f#(c(y, a, f(c(z, y, x)))) | | f#(f(c(a, y, z))) | → | b#(z, z) |
| c#(c(z, x, a), a, y) | → | f#(c(z, y, x)) | | c#(c(z, x, a), a, y) | → | c#(y, a, f(c(z, y, x))) |
| c#(c(z, x, a), a, y) | → | c#(z, y, x) | | c#(c(z, x, a), a, y) | → | f#(f(c(y, a, f(c(z, y, x))))) |
| f#(f(c(a, y, z))) | → | b#(y, b(z, z)) |
Rewrite Rules
| b(a, f(b(b(z, y), a))) | → | z | | c(c(z, x, a), a, y) | → | f(f(c(y, a, f(c(z, y, x))))) |
| f(f(c(a, y, z))) | → | b(y, b(z, z)) |
Original Signature
Termination of terms over the following signature is verified: f, b, c, a
Strategy
The following SCCs where found
| c#(c(z, x, a), a, y) → c#(y, a, f(c(z, y, x))) | c#(c(z, x, a), a, y) → c#(z, y, x) |