4.41/1.86	YES
4.61/1.87	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.61/1.87	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.61/1.87	
4.61/1.87	
4.61/1.87	Termination of the given C Problem could be proven:
4.61/1.87	
4.61/1.87	(0) C Problem
4.61/1.87	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.61/1.87	(2) IntTRS
4.61/1.87	(3) TerminationGraphProcessor [SOUND, 53 ms]
4.61/1.87	(4) IntTRS
4.61/1.87	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
4.61/1.87	(6) IntTRS
4.61/1.87	(7) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
4.61/1.87	(8) YES
4.61/1.87	
4.61/1.87	
4.61/1.87	----------------------------------------
4.61/1.87	
4.61/1.87	(0)
4.61/1.87	Obligation:
4.61/1.87	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.61/1.87	----------------------------------------
4.61/1.87	
4.61/1.87	(1) CToIRSProof (EQUIVALENT)
4.61/1.87	Parsed C Integer Program as IRS.
4.61/1.87	----------------------------------------
4.61/1.87	
4.61/1.87	(2)
4.61/1.87	Obligation:
4.61/1.87	Rules:
4.61/1.87	f1(x, y) -> f2(x_1, y) :|: TRUE
4.61/1.87	f2(x1, x2) -> f3(x1, x3) :|: TRUE
4.61/1.87	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 - 1
4.61/1.87	f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = x15 - 1
4.61/1.87	f3(x8, x9) -> f4(x8, x9) :|: x8 > 0 && x9 > 0
4.61/1.87	f6(x10, x11) -> f3(x10, x11) :|: TRUE
4.61/1.87	f3(x12, x13) -> f7(x12, x13) :|: x12 <= 0
4.61/1.87	f3(x17, x18) -> f7(x17, x18) :|: x18 <= 0
4.61/1.87	Start term: f1(x, y)
4.61/1.87	
4.61/1.87	----------------------------------------
4.61/1.87	
4.61/1.87	(3) TerminationGraphProcessor (SOUND)
4.61/1.87	Constructed the termination graph and obtained one non-trivial SCC.
4.61/1.87	
4.61/1.87	----------------------------------------
4.61/1.87	
4.61/1.87	(4)
4.61/1.87	Obligation:
4.61/1.87	Rules:
4.61/1.87	f3(x8, x9) -> f4(x8, x9) :|: x8 > 0 && x9 > 0
4.61/1.87	f6(x10, x11) -> f3(x10, x11) :|: TRUE
4.61/1.87	f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = x15 - 1
4.61/1.87	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 - 1
4.61/1.87	
4.61/1.87	----------------------------------------
4.61/1.87	
4.61/1.87	(5) IntTRSCompressionProof (EQUIVALENT)
4.61/1.87	Compressed rules.
4.61/1.87	----------------------------------------
4.61/1.87	
4.61/1.87	(6)
4.61/1.87	Obligation:
4.61/1.87	Rules:
4.61/1.87	f5(x14:0, x15:0) -> f5(x14:0 - 1, x15:0 - 1) :|: x14:0 > 0 && x15:0 > 1
4.61/1.87	
4.61/1.87	----------------------------------------
4.61/1.87	
4.61/1.87	(7) PolynomialOrderProcessor (EQUIVALENT)
4.61/1.87	Found the following polynomial interpretation:
4.61/1.87	[f5(x, x1)] = x1
4.61/1.87	
4.61/1.87	The following rules are decreasing:
4.61/1.87	f5(x14:0, x15:0) -> f5(x14:0 - 1, x15:0 - 1) :|: x14:0 > 0 && x15:0 > 1
4.61/1.87	The following rules are bounded:
4.61/1.87	f5(x14:0, x15:0) -> f5(x14:0 - 1, x15:0 - 1) :|: x14:0 > 0 && x15:0 > 1
4.61/1.87	
4.61/1.87	----------------------------------------
4.61/1.87	
4.61/1.87	(8)
4.61/1.87	YES
4.61/1.91	EOF