3.56/1.69	WORST_CASE(NON_POLY, ?)
3.56/1.70	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.56/1.70	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.56/1.70	
3.56/1.70	
3.56/1.70	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.56/1.70	
3.56/1.70	(0) CpxTRS
3.56/1.70	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.56/1.70	(2) TRS for Loop Detection
3.56/1.70	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
3.56/1.70	(4) BEST
3.56/1.70	    (5) proven lower bound
3.56/1.70	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
3.56/1.70	        (7) BOUNDS(n^1, INF)
3.56/1.70	    (8) TRS for Loop Detection
3.56/1.70	        (9) DecreasingLoopProof [FINISHED, 35 ms]
3.56/1.70	        (10) BOUNDS(EXP, INF)
3.56/1.70	
3.56/1.70	
3.56/1.70	----------------------------------------
3.56/1.70	
3.56/1.70	(0)
3.56/1.70	Obligation:
3.56/1.70	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.56/1.70	
3.56/1.70	
3.56/1.70	The TRS R consists of the following rules:
3.56/1.70	
3.56/1.70	   a__a -> a__c
3.56/1.70	   a__b -> a__c
3.56/1.70	   a__c -> e
3.56/1.70	   a__k -> l
3.56/1.70	   a__d -> m
3.56/1.70	   a__a -> a__d
3.56/1.70	   a__b -> a__d
3.56/1.70	   a__c -> l
3.56/1.70	   a__k -> m
3.56/1.70	   a__A -> a__h(a__f(a__a), a__f(a__b))
3.56/1.70	   a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k))
3.56/1.70	   a__g(d, X, X) -> a__A
3.56/1.70	   a__f(X) -> a__z(mark(X), X)
3.56/1.70	   a__z(e, X) -> mark(X)
3.56/1.70	   mark(A) -> a__A
3.56/1.70	   mark(a) -> a__a
3.56/1.70	   mark(b) -> a__b
3.56/1.70	   mark(c) -> a__c
3.56/1.70	   mark(d) -> a__d
3.56/1.70	   mark(k) -> a__k
3.56/1.70	   mark(z(X1, X2)) -> a__z(mark(X1), X2)
3.56/1.70	   mark(f(X)) -> a__f(mark(X))
3.56/1.70	   mark(h(X1, X2)) -> a__h(mark(X1), mark(X2))
3.56/1.70	   mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3))
3.56/1.70	   mark(e) -> e
3.56/1.70	   mark(l) -> l
3.56/1.70	   mark(m) -> m
3.56/1.70	   a__A -> A
3.56/1.70	   a__a -> a
3.56/1.70	   a__b -> b
3.56/1.70	   a__c -> c
3.56/1.70	   a__d -> d
3.56/1.70	   a__k -> k
3.56/1.70	   a__z(X1, X2) -> z(X1, X2)
3.56/1.70	   a__f(X) -> f(X)
3.56/1.70	   a__h(X1, X2) -> h(X1, X2)
3.56/1.70	   a__g(X1, X2, X3) -> g(X1, X2, X3)
3.56/1.70	
3.56/1.70	S is empty.
3.56/1.70	Rewrite Strategy: FULL
3.56/1.70	----------------------------------------
3.56/1.70	
3.56/1.70	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.56/1.70	Transformed a relative TRS into a decreasing-loop problem.
3.56/1.70	----------------------------------------
3.56/1.70	
3.56/1.70	(2)
3.56/1.70	Obligation:
3.56/1.70	Analyzing the following TRS for decreasing loops:
3.56/1.70	
3.56/1.70	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.56/1.70	
3.56/1.70	
3.56/1.70	The TRS R consists of the following rules:
3.56/1.70	
3.56/1.70	   a__a -> a__c
3.56/1.70	   a__b -> a__c
3.56/1.70	   a__c -> e
3.56/1.70	   a__k -> l
3.56/1.70	   a__d -> m
3.56/1.70	   a__a -> a__d
3.56/1.70	   a__b -> a__d
3.56/1.70	   a__c -> l
3.56/1.70	   a__k -> m
3.56/1.70	   a__A -> a__h(a__f(a__a), a__f(a__b))
3.56/1.70	   a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k))
3.56/1.70	   a__g(d, X, X) -> a__A
3.56/1.70	   a__f(X) -> a__z(mark(X), X)
3.56/1.70	   a__z(e, X) -> mark(X)
3.56/1.70	   mark(A) -> a__A
3.56/1.70	   mark(a) -> a__a
3.56/1.70	   mark(b) -> a__b
3.56/1.70	   mark(c) -> a__c
3.56/1.70	   mark(d) -> a__d
3.56/1.70	   mark(k) -> a__k
3.56/1.70	   mark(z(X1, X2)) -> a__z(mark(X1), X2)
3.56/1.70	   mark(f(X)) -> a__f(mark(X))
3.56/1.70	   mark(h(X1, X2)) -> a__h(mark(X1), mark(X2))
3.56/1.70	   mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3))
3.56/1.70	   mark(e) -> e
3.56/1.70	   mark(l) -> l
3.56/1.70	   mark(m) -> m
3.56/1.70	   a__A -> A
3.56/1.70	   a__a -> a
3.56/1.70	   a__b -> b
3.56/1.70	   a__c -> c
3.56/1.70	   a__d -> d
3.56/1.70	   a__k -> k
3.56/1.70	   a__z(X1, X2) -> z(X1, X2)
3.56/1.70	   a__f(X) -> f(X)
3.56/1.70	   a__h(X1, X2) -> h(X1, X2)
3.56/1.70	   a__g(X1, X2, X3) -> g(X1, X2, X3)
3.56/1.70	
3.56/1.70	S is empty.
3.56/1.70	Rewrite Strategy: FULL
3.56/1.70	----------------------------------------
3.56/1.70	
3.56/1.70	(3) DecreasingLoopProof (LOWER BOUND(ID))
3.56/1.70	The following loop(s) give(s) rise to the lower bound Omega(n^1):
3.56/1.70	
3.56/1.70	The rewrite sequence
3.56/1.70	
3.56/1.70	mark(z(X1, X2)) ->^+ a__z(mark(X1), X2)
3.56/1.70	
3.56/1.70	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
3.56/1.70	
3.56/1.70	The pumping substitution is [X1 / z(X1, X2)].
3.56/1.70	
3.56/1.70	The result substitution is [ ].
3.56/1.70	
3.56/1.70	
3.56/1.70	
3.56/1.70	
3.56/1.70	----------------------------------------
3.56/1.70	
3.56/1.70	(4)
3.56/1.70	Complex Obligation (BEST)
3.56/1.70	
3.56/1.70	----------------------------------------
3.56/1.70	
3.56/1.70	(5)
3.56/1.70	Obligation:
3.56/1.70	Proved the lower bound n^1 for the following obligation:
3.56/1.70	
3.56/1.70	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.56/1.70	
3.56/1.70	
3.56/1.70	The TRS R consists of the following rules:
3.56/1.70	
3.56/1.70	   a__a -> a__c
3.56/1.70	   a__b -> a__c
3.56/1.70	   a__c -> e
3.56/1.70	   a__k -> l
3.56/1.70	   a__d -> m
3.56/1.70	   a__a -> a__d
3.56/1.70	   a__b -> a__d
3.56/1.70	   a__c -> l
3.56/1.70	   a__k -> m
3.56/1.70	   a__A -> a__h(a__f(a__a), a__f(a__b))
3.56/1.70	   a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k))
3.56/1.70	   a__g(d, X, X) -> a__A
3.56/1.70	   a__f(X) -> a__z(mark(X), X)
3.56/1.70	   a__z(e, X) -> mark(X)
3.56/1.70	   mark(A) -> a__A
3.56/1.70	   mark(a) -> a__a
3.56/1.70	   mark(b) -> a__b
3.56/1.70	   mark(c) -> a__c
3.56/1.70	   mark(d) -> a__d
3.56/1.70	   mark(k) -> a__k
3.56/1.70	   mark(z(X1, X2)) -> a__z(mark(X1), X2)
3.56/1.70	   mark(f(X)) -> a__f(mark(X))
3.56/1.70	   mark(h(X1, X2)) -> a__h(mark(X1), mark(X2))
3.56/1.70	   mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3))
3.56/1.70	   mark(e) -> e
3.56/1.70	   mark(l) -> l
3.56/1.70	   mark(m) -> m
3.56/1.70	   a__A -> A
3.56/1.70	   a__a -> a
3.56/1.70	   a__b -> b
3.56/1.70	   a__c -> c
3.56/1.70	   a__d -> d
3.56/1.70	   a__k -> k
3.56/1.70	   a__z(X1, X2) -> z(X1, X2)
3.56/1.70	   a__f(X) -> f(X)
3.56/1.70	   a__h(X1, X2) -> h(X1, X2)
3.56/1.70	   a__g(X1, X2, X3) -> g(X1, X2, X3)
3.56/1.70	
3.56/1.70	S is empty.
3.56/1.70	Rewrite Strategy: FULL
3.56/1.70	----------------------------------------
3.56/1.70	
3.56/1.70	(6) LowerBoundPropagationProof (FINISHED)
3.56/1.70	Propagated lower bound.
3.56/1.70	----------------------------------------
3.56/1.70	
3.56/1.70	(7)
3.56/1.70	BOUNDS(n^1, INF)
3.56/1.70	
3.56/1.70	----------------------------------------
3.56/1.70	
3.56/1.70	(8)
3.56/1.70	Obligation:
3.56/1.70	Analyzing the following TRS for decreasing loops:
3.56/1.70	
3.56/1.70	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.56/1.70	
3.56/1.70	
3.56/1.70	The TRS R consists of the following rules:
3.56/1.70	
3.56/1.70	   a__a -> a__c
3.56/1.70	   a__b -> a__c
3.56/1.70	   a__c -> e
3.56/1.70	   a__k -> l
3.56/1.70	   a__d -> m
3.56/1.70	   a__a -> a__d
3.56/1.70	   a__b -> a__d
3.56/1.70	   a__c -> l
3.56/1.70	   a__k -> m
3.56/1.70	   a__A -> a__h(a__f(a__a), a__f(a__b))
3.56/1.70	   a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k))
3.56/1.70	   a__g(d, X, X) -> a__A
3.56/1.70	   a__f(X) -> a__z(mark(X), X)
3.56/1.70	   a__z(e, X) -> mark(X)
3.56/1.70	   mark(A) -> a__A
3.56/1.70	   mark(a) -> a__a
3.56/1.70	   mark(b) -> a__b
3.56/1.70	   mark(c) -> a__c
3.56/1.70	   mark(d) -> a__d
3.56/1.70	   mark(k) -> a__k
3.56/1.70	   mark(z(X1, X2)) -> a__z(mark(X1), X2)
3.56/1.70	   mark(f(X)) -> a__f(mark(X))
3.56/1.70	   mark(h(X1, X2)) -> a__h(mark(X1), mark(X2))
3.56/1.70	   mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3))
3.56/1.70	   mark(e) -> e
3.56/1.70	   mark(l) -> l
3.56/1.70	   mark(m) -> m
3.56/1.70	   a__A -> A
3.56/1.70	   a__a -> a
3.56/1.70	   a__b -> b
3.56/1.70	   a__c -> c
3.56/1.70	   a__d -> d
3.56/1.70	   a__k -> k
3.56/1.70	   a__z(X1, X2) -> z(X1, X2)
3.56/1.70	   a__f(X) -> f(X)
3.56/1.70	   a__h(X1, X2) -> h(X1, X2)
3.56/1.70	   a__g(X1, X2, X3) -> g(X1, X2, X3)
3.56/1.70	
3.56/1.70	S is empty.
3.56/1.70	Rewrite Strategy: FULL
3.56/1.70	----------------------------------------
3.56/1.70	
3.56/1.70	(9) DecreasingLoopProof (FINISHED)
3.56/1.70	The following loop(s) give(s) rise to the lower bound EXP:
3.56/1.70	
3.56/1.70	The rewrite sequence
3.56/1.70	
3.56/1.70	mark(f(X)) ->^+ a__z(mark(mark(X)), mark(X))
3.56/1.70	
3.56/1.70	gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0].
3.56/1.70	
3.56/1.70	The pumping substitution is [X / f(X)].
3.56/1.70	
3.56/1.70	The result substitution is [ ].
3.56/1.70	
3.56/1.70	
3.56/1.70	
3.56/1.70	The rewrite sequence
3.56/1.70	
3.56/1.70	mark(f(X)) ->^+ a__z(mark(mark(X)), mark(X))
3.56/1.70	
3.56/1.70	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
3.56/1.70	
3.56/1.70	The pumping substitution is [X / f(X)].
3.56/1.70	
3.56/1.70	The result substitution is [ ].
3.56/1.70	
3.56/1.70	
3.56/1.70	
3.56/1.70	
3.56/1.70	----------------------------------------
3.56/1.70	
3.56/1.70	(10)
3.56/1.70	BOUNDS(EXP, INF)
3.86/1.73	EOF