/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 0 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) TRUE


----------------------------------------

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   f(g(x), g(y)) -> f(p(f(g(x), s(y))), g(s(p(x))))
   p(0) -> g(0)
   g(s(p(x))) -> p(x)

Q is empty.

----------------------------------------

(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   F(g(x), g(y)) -> F(p(f(g(x), s(y))), g(s(p(x))))
   F(g(x), g(y)) -> P(f(g(x), s(y)))
   F(g(x), g(y)) -> F(g(x), s(y))
   F(g(x), g(y)) -> G(s(p(x)))
   F(g(x), g(y)) -> P(x)
   P(0) -> G(0)

The TRS R consists of the following rules:

   f(g(x), g(y)) -> f(p(f(g(x), s(y))), g(s(p(x))))
   p(0) -> g(0)
   g(s(p(x))) -> p(x)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(3) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 6 less nodes.
----------------------------------------

(4)
TRUE