3.24/1.54	WORST_CASE(?, O(1))
3.24/1.85	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.24/1.85	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.24/1.85	
3.24/1.85	
3.24/1.85	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.24/1.85	
3.24/1.85	(0) CpxTRS
3.24/1.85	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.24/1.85	(2) BOUNDS(1, 1)
3.24/1.85	
3.24/1.85	
3.24/1.85	----------------------------------------
3.24/1.85	
3.24/1.85	(0)
3.24/1.85	Obligation:
3.24/1.85	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.24/1.85	
3.24/1.85	
3.24/1.85	The TRS R consists of the following rules:
3.24/1.85	
3.24/1.85	   a__g(X) -> a__h(X)
3.24/1.85	   a__c -> d
3.24/1.85	   a__h(d) -> a__g(c)
3.24/1.85	   mark(g(X)) -> a__g(X)
3.24/1.85	   mark(h(X)) -> a__h(X)
3.24/1.85	   mark(c) -> a__c
3.24/1.85	   mark(d) -> d
3.24/1.85	   a__g(X) -> g(X)
3.24/1.85	   a__h(X) -> h(X)
3.24/1.85	   a__c -> c
3.24/1.85	
3.24/1.85	S is empty.
3.24/1.85	Rewrite Strategy: INNERMOST
3.24/1.85	----------------------------------------
3.24/1.85	
3.24/1.85	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.24/1.85	Constant runtime complexity proven by termination of constructor-based narrowing.
3.24/1.85	
3.24/1.85	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.24/1.85	
3.24/1.85	mark(d) ->^* d
3.24/1.85	
3.24/1.85	mark(c) ->^* c
3.24/1.85	
3.24/1.85	mark(c) ->^* d
3.24/1.85	
3.24/1.85	mark(h(x0)) ->^* h(x0)
3.24/1.85	
3.24/1.85	mark(h(d)) ->^* g(c)
3.24/1.85	
3.24/1.85	mark(h(d)) ->^* h(c)
3.24/1.85	
3.24/1.85	mark(g(x0)) ->^* g(x0)
3.24/1.85	
3.24/1.85	mark(g(x0)) ->^* h(x0)
3.24/1.85	
3.24/1.85	mark(g(d)) ->^* g(c)
3.24/1.85	
3.24/1.85	mark(g(d)) ->^* h(c)
3.24/1.85	
3.24/1.85	a__c ->^* c
3.24/1.85	
3.24/1.85	a__c ->^* d
3.24/1.85	
3.24/1.85	a__h(x0) ->^* h(x0)
3.24/1.85	
3.24/1.85	a__h(d) ->^* g(c)
3.24/1.85	
3.24/1.85	a__h(d) ->^* h(c)
3.24/1.85	
3.24/1.85	a__g(x0) ->^* g(x0)
3.24/1.85	
3.24/1.85	a__g(x0) ->^* h(x0)
3.24/1.85	
3.24/1.85	a__g(d) ->^* g(c)
3.24/1.85	
3.24/1.85	a__g(d) ->^* h(c)
3.24/1.85	
3.24/1.85	
3.24/1.85	
3.24/1.85	
3.24/1.85	----------------------------------------
3.24/1.85	
3.24/1.85	(2)
3.24/1.85	BOUNDS(1, 1)
3.24/1.88	EOF