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


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NO
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Outermost Termination of the given OTRS could be disproven:

(0) OTRS
(1) OutermostNonTerminationProof [COMPLETE, 54 ms]
(2) NO


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

   p(0) -> 0
   p(s(X)) -> X
   leq(0, Y) -> true
   leq(s(X), 0) -> false
   leq(s(X), s(Y)) -> leq(X, Y)
   if(true, X, Y) -> activate(X)
   if(false, X, Y) -> activate(Y)
   diff(X, Y) -> if(leq(X, Y), n__0, n__s(diff(p(X), Y)))
   0 -> n__0
   s(X) -> n__s(X)
   activate(n__0) -> 0
   activate(n__s(X)) -> s(X)
   activate(X) -> X



Outermost Strategy.

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(1) OutermostNonTerminationProof (COMPLETE)
Term rewrite system R:
The TRS R consists of the following rules:

   p(0) -> 0
   p(s(X)) -> X
   leq(0, Y) -> true
   leq(s(X), 0) -> false
   leq(s(X), s(Y)) -> leq(X, Y)
   if(true, X, Y) -> activate(X)
   if(false, X, Y) -> activate(Y)
   diff(X, Y) -> if(leq(X, Y), n__0, n__s(diff(p(X), Y)))
   0 -> n__0
   s(X) -> n__s(X)
   activate(n__0) -> 0
   activate(n__s(X)) -> s(X)
   activate(X) -> X



Outermost Strategy.

---------- Loop: ----------

diff(X, Y) -> if(leq(X, Y), n__0, n__s(diff(p(X), Y))) with rule diff(X', Y') -> if(leq(X', Y'), n__0, n__s(diff(p(X'), Y'))) at position [] and matcher [X' / X, Y' / Y]

Now an instance of the first term with Matcher [X / p(X)] occurs in the last term at position [2,0].

Context: if(leq(X, Y), n__0, n__s([]))

We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
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(2)
NO