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


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NO
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 39 ms]
(2) NO


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

   fact(X) -> if(zero(X), n__s(0), n__prod(X, fact(p(X))))
   add(0, X) -> X
   add(s(X), Y) -> s(add(X, Y))
   prod(0, X) -> 0
   prod(s(X), Y) -> add(Y, prod(X, Y))
   if(true, X, Y) -> activate(X)
   if(false, X, Y) -> activate(Y)
   zero(0) -> true
   zero(s(X)) -> false
   p(s(X)) -> X
   s(X) -> n__s(X)
   prod(X1, X2) -> n__prod(X1, X2)
   activate(n__s(X)) -> s(X)
   activate(n__prod(X1, X2)) -> prod(X1, X2)
   activate(X) -> X



Outermost Strategy.

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

   fact(X) -> if(zero(X), n__s(0), n__prod(X, fact(p(X))))
   add(0, X) -> X
   add(s(X), Y) -> s(add(X, Y))
   prod(0, X) -> 0
   prod(s(X), Y) -> add(Y, prod(X, Y))
   if(true, X, Y) -> activate(X)
   if(false, X, Y) -> activate(Y)
   zero(0) -> true
   zero(s(X)) -> false
   p(s(X)) -> X
   s(X) -> n__s(X)
   prod(X1, X2) -> n__prod(X1, X2)
   activate(n__s(X)) -> s(X)
   activate(n__prod(X1, X2)) -> prod(X1, X2)
   activate(X) -> X



Outermost Strategy.

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

fact(X) -> if(zero(X), n__s(0), n__prod(X, fact(p(X)))) with rule fact(X') -> if(zero(X'), n__s(0), n__prod(X', fact(p(X')))) at position [] and matcher [X' / X]

Now an instance of the first term with Matcher [X / p(X)] occurs in the last term at position [2,1].

Context: if(zero(X), n__s(0), n__prod(X, []))

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