4.23/1.96	YES
4.23/1.97	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.23/1.97	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.23/1.97	
4.23/1.97	
4.23/1.97	Termination of the given C Problem could be proven:
4.23/1.97	
4.23/1.97	(0) C Problem
4.23/1.97	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.23/1.97	(2) IntTRS
4.23/1.97	(3) TerminationGraphProcessor [SOUND, 50 ms]
4.23/1.97	(4) IntTRS
4.23/1.97	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
4.23/1.97	(6) IntTRS
4.23/1.97	(7) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
4.23/1.97	(8) YES
4.23/1.97	
4.23/1.97	
4.23/1.97	----------------------------------------
4.23/1.97	
4.23/1.97	(0)
4.23/1.97	Obligation:
4.23/1.97	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.23/1.97	----------------------------------------
4.23/1.97	
4.23/1.97	(1) CToIRSProof (EQUIVALENT)
4.23/1.97	Parsed C Integer Program as IRS.
4.23/1.97	----------------------------------------
4.23/1.97	
4.23/1.97	(2)
4.23/1.97	Obligation:
4.23/1.97	Rules:
4.23/1.97	f1(x, y) -> f2(x_1, y) :|: TRUE
4.23/1.97	f2(x1, x2) -> f3(x1, x3) :|: TRUE
4.23/1.97	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 + 1
4.23/1.97	f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = x15 + 2
4.23/1.97	f3(x8, x9) -> f4(x8, x9) :|: x8 > x9
4.23/1.97	f6(x10, x11) -> f3(x10, x11) :|: TRUE
4.23/1.97	f3(x12, x13) -> f7(x12, x13) :|: x12 <= x13
4.23/1.97	Start term: f1(x, y)
4.23/1.97	
4.23/1.97	----------------------------------------
4.23/1.97	
4.23/1.97	(3) TerminationGraphProcessor (SOUND)
4.23/1.97	Constructed the termination graph and obtained one non-trivial SCC.
4.23/1.97	
4.23/1.97	----------------------------------------
4.23/1.97	
4.23/1.97	(4)
4.23/1.97	Obligation:
4.23/1.97	Rules:
4.23/1.97	f3(x8, x9) -> f4(x8, x9) :|: x8 > x9
4.23/1.97	f6(x10, x11) -> f3(x10, x11) :|: TRUE
4.23/1.97	f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = x15 + 2
4.23/1.97	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 + 1
4.23/1.97	
4.23/1.97	----------------------------------------
4.23/1.97	
4.23/1.97	(5) IntTRSCompressionProof (EQUIVALENT)
4.23/1.97	Compressed rules.
4.23/1.97	----------------------------------------
4.23/1.97	
4.23/1.97	(6)
4.23/1.97	Obligation:
4.23/1.97	Rules:
4.23/1.97	f5(x14:0, x15:0) -> f5(x14:0 + 1, x15:0 + 2) :|: x15:0 + 2 < x14:0
4.23/1.97	
4.23/1.97	----------------------------------------
4.23/1.97	
4.23/1.97	(7) PolynomialOrderProcessor (EQUIVALENT)
4.23/1.97	Found the following polynomial interpretation:
4.23/1.97	[f5(x, x1)] = x - x1
4.23/1.97	
4.23/1.97	The following rules are decreasing:
4.23/1.97	f5(x14:0, x15:0) -> f5(x14:0 + 1, x15:0 + 2) :|: x15:0 + 2 < x14:0
4.23/1.97	The following rules are bounded:
4.23/1.97	f5(x14:0, x15:0) -> f5(x14:0 + 1, x15:0 + 2) :|: x15:0 + 2 < x14:0
4.23/1.97	
4.23/1.97	----------------------------------------
4.23/1.97	
4.23/1.97	(8)
4.23/1.97	YES
4.83/1.99	EOF