4.22/1.90	YES
4.22/1.91	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.22/1.91	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.22/1.91	
4.22/1.91	
4.22/1.91	Termination of the given C Problem could be proven:
4.22/1.91	
4.22/1.91	(0) C Problem
4.22/1.91	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.22/1.91	(2) IntTRS
4.22/1.91	(3) TerminationGraphProcessor [SOUND, 46 ms]
4.22/1.91	(4) IntTRS
4.22/1.91	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
4.22/1.91	(6) IntTRS
4.22/1.91	(7) PolynomialOrderProcessor [EQUIVALENT, 1 ms]
4.22/1.91	(8) YES
4.22/1.91	
4.22/1.91	
4.22/1.91	----------------------------------------
4.22/1.91	
4.22/1.91	(0)
4.22/1.91	Obligation:
4.22/1.91	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.22/1.91	----------------------------------------
4.22/1.91	
4.22/1.91	(1) CToIRSProof (EQUIVALENT)
4.22/1.91	Parsed C Integer Program as IRS.
4.22/1.91	----------------------------------------
4.22/1.91	
4.22/1.91	(2)
4.22/1.91	Obligation:
4.22/1.91	Rules:
4.22/1.91	f1(x, y) -> f2(x_1, y) :|: TRUE
4.22/1.91	f2(x1, x2) -> f3(x1, x3) :|: TRUE
4.22/1.91	f4(x4, x5) -> f5(x4, arith) :|: TRUE && arith = x5 + x4
4.22/1.91	f3(x6, x7) -> f4(x6, x7) :|: x6 > 0 && x6 > x7
4.22/1.91	f5(x8, x9) -> f3(x8, x9) :|: TRUE
4.22/1.91	f3(x10, x11) -> f6(x10, x11) :|: x10 <= 0
4.22/1.91	f3(x12, x13) -> f6(x12, x13) :|: x12 <= x13
4.22/1.91	Start term: f1(x, y)
4.22/1.91	
4.22/1.91	----------------------------------------
4.22/1.91	
4.22/1.91	(3) TerminationGraphProcessor (SOUND)
4.22/1.91	Constructed the termination graph and obtained one non-trivial SCC.
4.22/1.91	
4.22/1.91	----------------------------------------
4.22/1.91	
4.22/1.91	(4)
4.22/1.91	Obligation:
4.22/1.91	Rules:
4.22/1.91	f3(x6, x7) -> f4(x6, x7) :|: x6 > 0 && x6 > x7
4.22/1.91	f5(x8, x9) -> f3(x8, x9) :|: TRUE
4.22/1.91	f4(x4, x5) -> f5(x4, arith) :|: TRUE && arith = x5 + x4
4.22/1.91	
4.22/1.91	----------------------------------------
4.22/1.91	
4.22/1.91	(5) IntTRSCompressionProof (EQUIVALENT)
4.22/1.91	Compressed rules.
4.22/1.91	----------------------------------------
4.22/1.91	
4.22/1.91	(6)
4.22/1.91	Obligation:
4.22/1.91	Rules:
4.22/1.91	f5(x8:0, x9:0) -> f5(x8:0, x9:0 + x8:0) :|: x8:0 > 0 && x9:0 < x8:0
4.22/1.91	
4.22/1.91	----------------------------------------
4.22/1.91	
4.22/1.91	(7) PolynomialOrderProcessor (EQUIVALENT)
4.22/1.91	Found the following polynomial interpretation:
4.22/1.91	[f5(x, x1)] = x - x1
4.22/1.91	
4.22/1.91	The following rules are decreasing:
4.22/1.91	f5(x8:0, x9:0) -> f5(x8:0, x9:0 + x8:0) :|: x8:0 > 0 && x9:0 < x8:0
4.22/1.91	The following rules are bounded:
4.22/1.91	f5(x8:0, x9:0) -> f5(x8:0, x9:0 + x8:0) :|: x8:0 > 0 && x9:0 < x8:0
4.22/1.91	
4.22/1.91	----------------------------------------
4.22/1.91	
4.22/1.91	(8)
4.22/1.91	YES
4.54/1.94	EOF