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


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WORST_CASE(NON_POLY, ?)
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).

(0) CpxTRS
(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(2) TRS for Loop Detection
(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
(4) BOUNDS(INF, INF)


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(0)
Obligation:
The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).


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

S is empty.
Rewrite Strategy: FULL
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(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
Transformed a relative TRS into a decreasing-loop problem.
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(2)
Obligation:
Analyzing the following TRS for decreasing loops:

The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).


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

S is empty.
Rewrite Strategy: FULL
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(3) InfiniteLowerBoundProof (FINISHED)
The following loop proves infinite runtime complexity:

The rewrite sequence

fact(X) ->^+ if(zero(X), n__s(0), n__prod(X, fact(p(X))))

gives rise to a decreasing loop by considering the right hand sides subterm at position [2,1].

The pumping substitution is [ ].

The result substitution is [X / p(X)].




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(4)
BOUNDS(INF, INF)