3.21/1.55	WORST_CASE(?, O(1))
3.21/1.57	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.21/1.57	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.21/1.57	
3.21/1.57	
3.21/1.57	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.21/1.57	
3.21/1.57	(0) CpxTRS
3.21/1.57	(1) DependencyGraphProof [UPPER BOUND(ID), 0 ms]
3.21/1.57	(2) CpxTRS
3.21/1.57	(3) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.21/1.57	(4) BOUNDS(1, 1)
3.21/1.57	
3.21/1.57	
3.21/1.57	----------------------------------------
3.21/1.57	
3.21/1.57	(0)
3.21/1.57	Obligation:
3.21/1.57	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.21/1.57	
3.21/1.57	
3.21/1.57	The TRS R consists of the following rules:
3.21/1.57	
3.21/1.57	   *(i(x), x) -> 1
3.21/1.57	   *(1, y) -> y
3.21/1.57	   *(x, 0) -> 0
3.21/1.57	   *(*(x, y), z) -> *(x, *(y, z))
3.21/1.57	
3.21/1.57	S is empty.
3.21/1.57	Rewrite Strategy: FULL
3.21/1.57	----------------------------------------
3.21/1.57	
3.21/1.57	(1) DependencyGraphProof (UPPER BOUND(ID))
3.21/1.57	The following rules are not reachable from basic terms in the dependency graph and can be removed:
3.21/1.57	
3.21/1.57	*(*(x, y), z) -> *(x, *(y, z))
3.21/1.57	
3.21/1.57	----------------------------------------
3.21/1.57	
3.21/1.57	(2)
3.21/1.57	Obligation:
3.21/1.57	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.21/1.57	
3.21/1.57	
3.21/1.57	The TRS R consists of the following rules:
3.21/1.57	
3.21/1.57	   *(i(x), x) -> 1
3.21/1.57	   *(1, y) -> y
3.21/1.57	   *(x, 0) -> 0
3.21/1.57	
3.21/1.57	S is empty.
3.21/1.57	Rewrite Strategy: FULL
3.21/1.57	----------------------------------------
3.21/1.57	
3.21/1.57	(3) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.21/1.57	Constant runtime complexity proven by termination of constructor-based narrowing.
3.21/1.57	
3.21/1.57	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.21/1.57	
3.21/1.57	*(x0, 0) ->^* 0
3.21/1.57	
3.21/1.57	*(i(x0), x0) ->^* 1
3.21/1.57	
3.21/1.57	
3.21/1.57	
3.21/1.57	
3.21/1.57	----------------------------------------
3.21/1.57	
3.21/1.57	(4)
3.21/1.57	BOUNDS(1, 1)
3.21/1.61	EOF