4.32/1.80	YES
4.38/1.81	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.38/1.81	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.38/1.81	
4.38/1.81	
4.38/1.81	Termination of the given C Problem could be proven:
4.38/1.81	
4.38/1.81	(0) C Problem
4.38/1.81	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.38/1.81	(2) IntTRS
4.38/1.81	(3) TerminationGraphProcessor [SOUND, 27 ms]
4.38/1.81	(4) IntTRS
4.38/1.81	(5) IntTRSCompressionProof [EQUIVALENT, 32 ms]
4.38/1.81	(6) IntTRS
4.38/1.81	(7) RankingReductionPairProof [EQUIVALENT, 19 ms]
4.38/1.81	(8) YES
4.38/1.81	
4.38/1.81	
4.38/1.81	----------------------------------------
4.38/1.81	
4.38/1.81	(0)
4.38/1.81	Obligation:
4.38/1.81	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.38/1.81	----------------------------------------
4.38/1.81	
4.38/1.81	(1) CToIRSProof (EQUIVALENT)
4.38/1.81	Parsed C Integer Program as IRS.
4.38/1.81	----------------------------------------
4.38/1.81	
4.38/1.81	(2)
4.38/1.81	Obligation:
4.38/1.81	Rules:
4.38/1.81	f1(y) -> f2(x_1) :|: TRUE
4.38/1.81	f3(x) -> f4(arith) :|: TRUE && arith = x - 1
4.38/1.81	f2(x1) -> f3(x1) :|: x1 >= 0
4.38/1.81	f4(x2) -> f2(x2) :|: TRUE
4.38/1.81	f2(x3) -> f5(x3) :|: x3 < 0
4.38/1.81	Start term: f1(y)
4.38/1.81	
4.38/1.81	----------------------------------------
4.38/1.81	
4.38/1.81	(3) TerminationGraphProcessor (SOUND)
4.38/1.81	Constructed the termination graph and obtained one non-trivial SCC.
4.38/1.81	
4.38/1.81	----------------------------------------
4.38/1.81	
4.38/1.81	(4)
4.38/1.81	Obligation:
4.38/1.81	Rules:
4.38/1.81	f2(x1) -> f3(x1) :|: x1 >= 0
4.38/1.81	f4(x2) -> f2(x2) :|: TRUE
4.38/1.81	f3(x) -> f4(arith) :|: TRUE && arith = x - 1
4.38/1.81	
4.38/1.81	----------------------------------------
4.38/1.81	
4.38/1.81	(5) IntTRSCompressionProof (EQUIVALENT)
4.38/1.81	Compressed rules.
4.38/1.81	----------------------------------------
4.38/1.81	
4.38/1.81	(6)
4.38/1.81	Obligation:
4.38/1.81	Rules:
4.38/1.81	f4(x2:0) -> f4(x2:0 - 1) :|: x2:0 > -1
4.38/1.81	
4.38/1.81	----------------------------------------
4.38/1.81	
4.38/1.81	(7) RankingReductionPairProof (EQUIVALENT)
4.38/1.81	Interpretation:
4.38/1.81	[ f4 ] = f4_1
4.38/1.81	
4.38/1.81	The following rules are decreasing:
4.38/1.81	f4(x2:0) -> f4(x2:0 - 1) :|: x2:0 > -1
4.38/1.81	
4.38/1.81	The following rules are bounded:
4.38/1.81	f4(x2:0) -> f4(x2:0 - 1) :|: x2:0 > -1
4.38/1.81	
4.38/1.81	
4.38/1.81	----------------------------------------
4.38/1.81	
4.38/1.81	(8)
4.38/1.81	YES
4.43/1.83	EOF