4.41/1.95	YES
4.41/1.96	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.41/1.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.41/1.96	
4.41/1.96	
4.41/1.96	Termination of the given C Problem could be proven:
4.41/1.96	
4.41/1.96	(0) C Problem
4.41/1.96	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.41/1.96	(2) IntTRS
4.41/1.96	(3) TerminationGraphProcessor [SOUND, 20 ms]
4.41/1.96	(4) IntTRS
4.41/1.96	(5) IntTRSCompressionProof [EQUIVALENT, 25 ms]
4.41/1.96	(6) IntTRS
4.41/1.96	(7) RankingReductionPairProof [EQUIVALENT, 0 ms]
4.41/1.96	(8) YES
4.41/1.96	
4.41/1.96	
4.41/1.96	----------------------------------------
4.41/1.96	
4.41/1.96	(0)
4.41/1.96	Obligation:
4.41/1.96	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.41/1.96	----------------------------------------
4.41/1.96	
4.41/1.96	(1) CToIRSProof (EQUIVALENT)
4.41/1.96	Parsed C Integer Program as IRS.
4.41/1.96	----------------------------------------
4.41/1.96	
4.41/1.96	(2)
4.41/1.96	Obligation:
4.41/1.96	Rules:
4.41/1.96	f1(x, y) -> f2(x_1, y) :|: TRUE
4.41/1.96	f2(x1, x2) -> f3(x1, x3) :|: TRUE
4.41/1.96	f4(x4, x5) -> f5(x4, arith) :|: TRUE && arith = x5 + 1
4.41/1.96	f3(x6, x7) -> f4(x6, x7) :|: x6 >= x7 + 1
4.41/1.96	f5(x8, x9) -> f3(x8, x9) :|: TRUE
4.41/1.96	f3(x10, x11) -> f6(x10, x11) :|: x10 < x11 + 1
4.41/1.96	Start term: f1(x, y)
4.41/1.96	
4.41/1.96	----------------------------------------
4.41/1.96	
4.41/1.96	(3) TerminationGraphProcessor (SOUND)
4.41/1.96	Constructed the termination graph and obtained one non-trivial SCC.
4.41/1.96	
4.41/1.96	----------------------------------------
4.41/1.96	
4.41/1.96	(4)
4.41/1.96	Obligation:
4.41/1.96	Rules:
4.41/1.96	f3(x6, x7) -> f4(x6, x7) :|: x6 >= x7 + 1
4.41/1.96	f5(x8, x9) -> f3(x8, x9) :|: TRUE
4.41/1.96	f4(x4, x5) -> f5(x4, arith) :|: TRUE && arith = x5 + 1
4.41/1.96	
4.41/1.96	----------------------------------------
4.41/1.96	
4.41/1.96	(5) IntTRSCompressionProof (EQUIVALENT)
4.41/1.96	Compressed rules.
4.41/1.96	----------------------------------------
4.41/1.96	
4.41/1.96	(6)
4.41/1.96	Obligation:
4.41/1.96	Rules:
4.41/1.96	f5(x8:0, x9:0) -> f5(x8:0, x9:0 + 1) :|: x9:0 + 1 <= x8:0
4.41/1.96	
4.41/1.96	----------------------------------------
4.41/1.96	
4.41/1.96	(7) RankingReductionPairProof (EQUIVALENT)
4.41/1.96	Interpretation:
4.41/1.96	[ f5 ] = -1*f5_2 + f5_1
4.41/1.96	
4.41/1.96	The following rules are decreasing:
4.41/1.96	f5(x8:0, x9:0) -> f5(x8:0, x9:0 + 1) :|: x9:0 + 1 <= x8:0
4.41/1.96	
4.41/1.96	The following rules are bounded:
4.41/1.96	f5(x8:0, x9:0) -> f5(x8:0, x9:0 + 1) :|: x9:0 + 1 <= x8:0
4.41/1.96	
4.41/1.96	
4.41/1.96	----------------------------------------
4.41/1.96	
4.41/1.96	(8)
4.41/1.96	YES
4.41/1.99	EOF