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


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YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Quasi decreasingness of the given CTRS could be proven:

(0) CTRS
(1) CTRSToQTRSProof [SOUND, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 0 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) TRUE


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(0)
Obligation:
Conditional term rewrite system:
The TRS R consists of the following rules:

   p(q(x)) -> p(r(x))
   q(h(x)) -> r(x)
   s(x) -> 1

The conditional TRS C consists of the following conditional rules:

   r(x) -> r(h(x)) <= s(x) -> 0


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(1) CTRSToQTRSProof (SOUND)
The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC].
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(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   r(x) -> U1(s(x), x)
   U1(0, x) -> r(h(x))
   p(q(x)) -> p(r(x))
   q(h(x)) -> r(x)
   s(x) -> 1

Q is empty.

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(3) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
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(4)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   R(x) -> U1^1(s(x), x)
   R(x) -> S(x)
   U1^1(0, x) -> R(h(x))
   P(q(x)) -> P(r(x))
   P(q(x)) -> R(x)
   Q(h(x)) -> R(x)

The TRS R consists of the following rules:

   r(x) -> U1(s(x), x)
   U1(0, x) -> r(h(x))
   p(q(x)) -> p(r(x))
   q(h(x)) -> r(x)
   s(x) -> 1

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
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(5) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 6 less nodes.
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(6)
TRUE