6.47/2.42	WORST_CASE(NON_POLY, ?)
6.47/2.42	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
6.47/2.42	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.47/2.42	
6.47/2.42	
6.47/2.42	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
6.47/2.42	
6.47/2.42	(0) CpxTRS
6.47/2.42	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
6.47/2.42	(2) TRS for Loop Detection
6.47/2.42	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
6.47/2.42	(4) BEST
6.47/2.42	    (5) proven lower bound
6.47/2.42	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
6.47/2.42	        (7) BOUNDS(n^1, INF)
6.47/2.42	    (8) TRS for Loop Detection
6.47/2.42	        (9) DecreasingLoopProof [FINISHED, 543 ms]
6.47/2.42	        (10) BOUNDS(EXP, INF)
6.47/2.42	
6.47/2.42	
6.47/2.42	----------------------------------------
6.47/2.42	
6.47/2.42	(0)
6.47/2.42	Obligation:
6.47/2.42	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
6.47/2.42	
6.47/2.42	
6.47/2.42	The TRS R consists of the following rules:
6.47/2.42	
6.47/2.42	   select(x', revprefix, Cons(x, xs)) -> mapconsapp(x', permute(revapp(revprefix, Cons(x, xs))), select(x, Cons(x', revprefix), xs))
6.47/2.42	   revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest))
6.47/2.42	   permute(Cons(x, xs)) -> select(x, Nil, xs)
6.47/2.42	   mapconsapp(x', Cons(x, xs), rest) -> Cons(Cons(x', x), mapconsapp(x', xs, rest))
6.47/2.42	   select(x, revprefix, Nil) -> mapconsapp(x, permute(revapp(revprefix, Nil)), Nil)
6.47/2.42	   revapp(Nil, rest) -> rest
6.47/2.42	   permute(Nil) -> Cons(Nil, Nil)
6.47/2.42	   mapconsapp(x, Nil, rest) -> rest
6.47/2.42	   goal(xs) -> permute(xs)
6.47/2.42	
6.47/2.42	S is empty.
6.47/2.42	Rewrite Strategy: INNERMOST
6.47/2.42	----------------------------------------
6.47/2.42	
6.47/2.42	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
6.47/2.42	Transformed a relative TRS into a decreasing-loop problem.
6.47/2.42	----------------------------------------
6.47/2.42	
6.47/2.42	(2)
6.47/2.42	Obligation:
6.47/2.42	Analyzing the following TRS for decreasing loops:
6.47/2.42	
6.47/2.42	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
6.47/2.42	
6.47/2.42	
6.47/2.42	The TRS R consists of the following rules:
6.47/2.42	
6.47/2.42	   select(x', revprefix, Cons(x, xs)) -> mapconsapp(x', permute(revapp(revprefix, Cons(x, xs))), select(x, Cons(x', revprefix), xs))
6.47/2.42	   revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest))
6.47/2.42	   permute(Cons(x, xs)) -> select(x, Nil, xs)
6.47/2.42	   mapconsapp(x', Cons(x, xs), rest) -> Cons(Cons(x', x), mapconsapp(x', xs, rest))
6.47/2.42	   select(x, revprefix, Nil) -> mapconsapp(x, permute(revapp(revprefix, Nil)), Nil)
6.47/2.42	   revapp(Nil, rest) -> rest
6.47/2.42	   permute(Nil) -> Cons(Nil, Nil)
6.47/2.42	   mapconsapp(x, Nil, rest) -> rest
6.47/2.42	   goal(xs) -> permute(xs)
6.47/2.42	
6.47/2.42	S is empty.
6.47/2.42	Rewrite Strategy: INNERMOST
6.47/2.42	----------------------------------------
6.47/2.42	
6.47/2.42	(3) DecreasingLoopProof (LOWER BOUND(ID))
6.47/2.42	The following loop(s) give(s) rise to the lower bound Omega(n^1):
6.47/2.42	
6.47/2.42	The rewrite sequence
6.47/2.42	
6.47/2.42	revapp(Cons(x, xs), rest) ->^+ revapp(xs, Cons(x, rest))
6.47/2.42	
6.47/2.42	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
6.47/2.42	
6.47/2.42	The pumping substitution is [xs / Cons(x, xs)].
6.47/2.42	
6.47/2.42	The result substitution is [rest / Cons(x, rest)].
6.47/2.42	
6.47/2.42	
6.47/2.42	
6.47/2.42	
6.47/2.42	----------------------------------------
6.47/2.42	
6.47/2.42	(4)
6.47/2.42	Complex Obligation (BEST)
6.47/2.42	
6.47/2.42	----------------------------------------
6.47/2.42	
6.47/2.42	(5)
6.47/2.42	Obligation:
6.47/2.42	Proved the lower bound n^1 for the following obligation:
6.47/2.42	
6.47/2.42	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
6.47/2.42	
6.47/2.42	
6.47/2.42	The TRS R consists of the following rules:
6.47/2.42	
6.47/2.42	   select(x', revprefix, Cons(x, xs)) -> mapconsapp(x', permute(revapp(revprefix, Cons(x, xs))), select(x, Cons(x', revprefix), xs))
6.47/2.42	   revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest))
6.47/2.42	   permute(Cons(x, xs)) -> select(x, Nil, xs)
6.47/2.42	   mapconsapp(x', Cons(x, xs), rest) -> Cons(Cons(x', x), mapconsapp(x', xs, rest))
6.47/2.42	   select(x, revprefix, Nil) -> mapconsapp(x, permute(revapp(revprefix, Nil)), Nil)
6.47/2.42	   revapp(Nil, rest) -> rest
6.47/2.42	   permute(Nil) -> Cons(Nil, Nil)
6.47/2.42	   mapconsapp(x, Nil, rest) -> rest
6.47/2.42	   goal(xs) -> permute(xs)
6.47/2.42	
6.47/2.42	S is empty.
6.47/2.42	Rewrite Strategy: INNERMOST
6.47/2.42	----------------------------------------
6.47/2.42	
6.47/2.42	(6) LowerBoundPropagationProof (FINISHED)
6.47/2.42	Propagated lower bound.
6.47/2.42	----------------------------------------
6.47/2.42	
6.47/2.42	(7)
6.47/2.42	BOUNDS(n^1, INF)
6.47/2.42	
6.47/2.42	----------------------------------------
6.47/2.42	
6.47/2.42	(8)
6.47/2.42	Obligation:
6.47/2.42	Analyzing the following TRS for decreasing loops:
6.47/2.42	
6.47/2.42	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
6.47/2.42	
6.47/2.42	
6.47/2.42	The TRS R consists of the following rules:
6.47/2.42	
6.47/2.42	   select(x', revprefix, Cons(x, xs)) -> mapconsapp(x', permute(revapp(revprefix, Cons(x, xs))), select(x, Cons(x', revprefix), xs))
6.47/2.42	   revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest))
6.47/2.42	   permute(Cons(x, xs)) -> select(x, Nil, xs)
6.47/2.42	   mapconsapp(x', Cons(x, xs), rest) -> Cons(Cons(x', x), mapconsapp(x', xs, rest))
6.47/2.42	   select(x, revprefix, Nil) -> mapconsapp(x, permute(revapp(revprefix, Nil)), Nil)
6.47/2.42	   revapp(Nil, rest) -> rest
6.47/2.42	   permute(Nil) -> Cons(Nil, Nil)
6.47/2.42	   mapconsapp(x, Nil, rest) -> rest
6.47/2.42	   goal(xs) -> permute(xs)
6.47/2.42	
6.47/2.42	S is empty.
6.47/2.42	Rewrite Strategy: INNERMOST
6.47/2.42	----------------------------------------
6.47/2.42	
6.47/2.42	(9) DecreasingLoopProof (FINISHED)
6.47/2.42	The following loop(s) give(s) rise to the lower bound EXP:
6.47/2.42	
6.47/2.42	The rewrite sequence
6.47/2.42	
6.47/2.42	permute(Cons(x, Cons(x3_0, Cons(x3_1, xs4_1)))) ->^+ mapconsapp(x, permute(Cons(x3_0, Cons(x3_1, xs4_1))), mapconsapp(x3_0, permute(Cons(x, Cons(x3_1, xs4_1))), select(x3_1, Cons(x3_0, Cons(x, Nil)), xs4_1)))
6.47/2.42	
6.47/2.42	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
6.47/2.42	
6.47/2.42	The pumping substitution is [xs4_1 / Cons(x3_1, xs4_1)].
6.47/2.42	
6.47/2.42	The result substitution is [x / x3_0, x3_0 / x3_1].
6.47/2.42	
6.47/2.42	
6.47/2.42	
6.47/2.42	The rewrite sequence
6.47/2.42	
6.47/2.42	permute(Cons(x, Cons(x3_0, Cons(x3_1, xs4_1)))) ->^+ mapconsapp(x, permute(Cons(x3_0, Cons(x3_1, xs4_1))), mapconsapp(x3_0, permute(Cons(x, Cons(x3_1, xs4_1))), select(x3_1, Cons(x3_0, Cons(x, Nil)), xs4_1)))
6.47/2.42	
6.47/2.42	gives rise to a decreasing loop by considering the right hand sides subterm at position [2,1].
6.47/2.42	
6.47/2.42	The pumping substitution is [xs4_1 / Cons(x3_1, xs4_1)].
6.47/2.42	
6.47/2.42	The result substitution is [x3_0 / x3_1].
6.47/2.42	
6.47/2.42	
6.47/2.42	
6.47/2.42	
6.47/2.42	----------------------------------------
6.47/2.42	
6.47/2.42	(10)
6.47/2.42	BOUNDS(EXP, INF)
6.56/2.46	EOF