3.17/1.73	WORST_CASE(?, O(1))
3.17/1.74	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.17/1.74	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.17/1.74	
3.17/1.74	
3.17/1.74	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.17/1.74	
3.17/1.74	(0) CpxTRS
3.17/1.74	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.17/1.74	(2) BOUNDS(1, 1)
3.17/1.74	
3.17/1.74	
3.17/1.74	----------------------------------------
3.17/1.74	
3.17/1.74	(0)
3.17/1.74	Obligation:
3.17/1.74	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.17/1.74	
3.17/1.74	
3.17/1.74	The TRS R consists of the following rules:
3.17/1.74	
3.17/1.74	   a__c -> a__f(g(c))
3.17/1.74	   a__f(g(X)) -> g(X)
3.17/1.74	   mark(c) -> a__c
3.17/1.74	   mark(f(X)) -> a__f(X)
3.17/1.74	   mark(g(X)) -> g(X)
3.17/1.74	   a__c -> c
3.17/1.74	   a__f(X) -> f(X)
3.17/1.74	
3.17/1.74	S is empty.
3.17/1.74	Rewrite Strategy: FULL
3.17/1.74	----------------------------------------
3.17/1.74	
3.17/1.74	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.17/1.74	Constant runtime complexity proven by termination of constructor-based narrowing.
3.17/1.74	
3.17/1.74	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.17/1.74	
3.17/1.74	mark(g(x0)) ->^* g(x0)
3.17/1.74	
3.17/1.74	mark(f(x0)) ->^* f(x0)
3.17/1.74	
3.17/1.74	mark(f(g(x0))) ->^* g(x0)
3.17/1.74	
3.17/1.74	mark(c) ->^* c
3.17/1.74	
3.17/1.74	mark(c) ->^* f(g(c))
3.17/1.74	
3.17/1.74	mark(c) ->^* g(c)
3.17/1.74	
3.17/1.74	a__c ->^* c
3.17/1.74	
3.17/1.74	a__c ->^* f(g(c))
3.17/1.74	
3.17/1.74	a__c ->^* g(c)
3.17/1.74	
3.17/1.74	a__f(x0) ->^* f(x0)
3.17/1.74	
3.17/1.74	a__f(g(x0)) ->^* g(x0)
3.17/1.74	
3.17/1.74	
3.17/1.74	
3.17/1.74	
3.17/1.74	----------------------------------------
3.17/1.74	
3.17/1.74	(2)
3.17/1.74	BOUNDS(1, 1)
3.17/1.78	EOF