2.96/1.50	WORST_CASE(?, O(1))
2.96/1.50	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.96/1.50	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.96/1.50	
2.96/1.50	
2.96/1.50	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.96/1.50	
2.96/1.50	(0) CpxTRS
2.96/1.50	(1) DependencyGraphProof [UPPER BOUND(ID), 0 ms]
2.96/1.50	(2) CpxTRS
2.96/1.50	(3) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
2.96/1.50	(4) BOUNDS(1, 1)
2.96/1.50	
2.96/1.50	
2.96/1.50	----------------------------------------
2.96/1.50	
2.96/1.50	(0)
2.96/1.50	Obligation:
2.96/1.50	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.96/1.50	
2.96/1.50	
2.96/1.50	The TRS R consists of the following rules:
2.96/1.50	
2.96/1.50	   +(x, 0) -> x
2.96/1.50	   +(x, i(x)) -> 0
2.96/1.50	   +(+(x, y), z) -> +(x, +(y, z))
2.96/1.50	   *(x, +(y, z)) -> +(*(x, y), *(x, z))
2.96/1.50	   *(+(x, y), z) -> +(*(x, z), *(y, z))
2.96/1.50	
2.96/1.50	S is empty.
2.96/1.50	Rewrite Strategy: FULL
2.96/1.50	----------------------------------------
2.96/1.50	
2.96/1.50	(1) DependencyGraphProof (UPPER BOUND(ID))
2.96/1.50	The following rules are not reachable from basic terms in the dependency graph and can be removed:
2.96/1.50	
2.96/1.50	+(+(x, y), z) -> +(x, +(y, z))
2.96/1.50	*(x, +(y, z)) -> +(*(x, y), *(x, z))
2.96/1.50	*(+(x, y), z) -> +(*(x, z), *(y, z))
2.96/1.50	
2.96/1.50	----------------------------------------
2.96/1.50	
2.96/1.50	(2)
2.96/1.50	Obligation:
2.96/1.50	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.96/1.50	
2.96/1.50	
2.96/1.50	The TRS R consists of the following rules:
2.96/1.50	
2.96/1.50	   +(x, 0) -> x
2.96/1.50	   +(x, i(x)) -> 0
2.96/1.50	
2.96/1.50	S is empty.
2.96/1.50	Rewrite Strategy: FULL
2.96/1.50	----------------------------------------
2.96/1.50	
2.96/1.50	(3) NarrowingOnBasicTermsTerminatesProof (FINISHED)
2.96/1.50	Constant runtime complexity proven by termination of constructor-based narrowing.
2.96/1.50	
2.96/1.50	The maximal most general narrowing sequences give rise to the following rewrite sequences:
2.96/1.50	
2.96/1.50	+(x0, i(x0)) ->^* 0
2.96/1.50	
2.96/1.50	
2.96/1.50	
2.96/1.50	
2.96/1.50	----------------------------------------
2.96/1.50	
2.96/1.50	(4)
2.96/1.50	BOUNDS(1, 1)
3.05/1.53	EOF