2.77/1.56	WORST_CASE(NON_POLY, ?)
2.77/1.57	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.77/1.57	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.77/1.57	
2.77/1.57	
2.77/1.57	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.77/1.57	
2.77/1.57	(0) CpxTRS
2.77/1.57	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
2.77/1.57	(2) TRS for Loop Detection
2.77/1.57	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
2.77/1.57	(4) BOUNDS(INF, INF)
2.77/1.57	
2.77/1.57	
2.77/1.57	----------------------------------------
2.77/1.57	
2.77/1.57	(0)
2.77/1.57	Obligation:
2.77/1.57	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.77/1.57	
2.77/1.57	
2.77/1.57	The TRS R consists of the following rules:
2.77/1.57	
2.77/1.57	   fact(X) -> if(zero(X), n__s(0), n__prod(X, fact(p(X))))
2.77/1.57	   add(0, X) -> X
2.77/1.57	   add(s(X), Y) -> s(add(X, Y))
2.77/1.57	   prod(0, X) -> 0
2.77/1.57	   prod(s(X), Y) -> add(Y, prod(X, Y))
2.77/1.57	   if(true, X, Y) -> activate(X)
2.77/1.57	   if(false, X, Y) -> activate(Y)
2.77/1.57	   zero(0) -> true
2.77/1.57	   zero(s(X)) -> false
2.77/1.57	   p(s(X)) -> X
2.77/1.57	   s(X) -> n__s(X)
2.77/1.57	   prod(X1, X2) -> n__prod(X1, X2)
2.77/1.57	   activate(n__s(X)) -> s(X)
2.77/1.57	   activate(n__prod(X1, X2)) -> prod(X1, X2)
2.77/1.57	   activate(X) -> X
2.77/1.57	
2.77/1.57	S is empty.
2.77/1.57	Rewrite Strategy: FULL
2.77/1.57	----------------------------------------
2.77/1.57	
2.77/1.57	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
2.77/1.57	Transformed a relative TRS into a decreasing-loop problem.
2.77/1.57	----------------------------------------
2.77/1.57	
2.77/1.57	(2)
2.77/1.57	Obligation:
2.77/1.57	Analyzing the following TRS for decreasing loops:
2.77/1.57	
2.77/1.57	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.77/1.57	
2.77/1.57	
2.77/1.57	The TRS R consists of the following rules:
2.77/1.57	
2.77/1.57	   fact(X) -> if(zero(X), n__s(0), n__prod(X, fact(p(X))))
2.77/1.57	   add(0, X) -> X
2.77/1.57	   add(s(X), Y) -> s(add(X, Y))
2.77/1.57	   prod(0, X) -> 0
2.77/1.57	   prod(s(X), Y) -> add(Y, prod(X, Y))
2.77/1.57	   if(true, X, Y) -> activate(X)
2.77/1.57	   if(false, X, Y) -> activate(Y)
2.77/1.57	   zero(0) -> true
2.77/1.57	   zero(s(X)) -> false
2.77/1.57	   p(s(X)) -> X
2.77/1.57	   s(X) -> n__s(X)
2.77/1.57	   prod(X1, X2) -> n__prod(X1, X2)
2.77/1.57	   activate(n__s(X)) -> s(X)
2.77/1.57	   activate(n__prod(X1, X2)) -> prod(X1, X2)
2.77/1.57	   activate(X) -> X
2.77/1.57	
2.77/1.57	S is empty.
2.77/1.57	Rewrite Strategy: FULL
2.77/1.57	----------------------------------------
2.77/1.57	
2.77/1.57	(3) InfiniteLowerBoundProof (FINISHED)
2.77/1.57	The following loop proves infinite runtime complexity:
2.77/1.57	
2.77/1.57	The rewrite sequence
2.77/1.57	
2.77/1.57	fact(X) ->^+ if(zero(X), n__s(0), n__prod(X, fact(p(X))))
2.77/1.57	
2.77/1.57	gives rise to a decreasing loop by considering the right hand sides subterm at position [2,1].
2.77/1.57	
2.77/1.57	The pumping substitution is [ ].
2.77/1.57	
2.77/1.57	The result substitution is [X / p(X)].
2.77/1.57	
2.77/1.57	
2.77/1.57	
2.77/1.57	
2.77/1.57	----------------------------------------
2.77/1.57	
2.77/1.57	(4)
2.77/1.57	BOUNDS(INF, INF)
2.98/1.61	EOF