4.27/1.92	YES
4.27/1.93	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.27/1.93	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.27/1.93	
4.27/1.93	
4.27/1.93	Termination of the given C Problem could be proven:
4.27/1.93	
4.27/1.93	(0) C Problem
4.27/1.93	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.27/1.93	(2) IntTRS
4.27/1.93	(3) TerminationGraphProcessor [SOUND, 28 ms]
4.27/1.93	(4) IntTRS
4.27/1.93	(5) IntTRSCompressionProof [EQUIVALENT, 9 ms]
4.27/1.93	(6) IntTRS
4.27/1.93	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.27/1.93	(8) IntTRS
4.27/1.93	(9) PolynomialOrderProcessor [EQUIVALENT, 11 ms]
4.27/1.93	(10) YES
4.27/1.93	
4.27/1.93	
4.27/1.93	----------------------------------------
4.27/1.93	
4.27/1.93	(0)
4.27/1.93	Obligation:
4.27/1.93	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.27/1.93	----------------------------------------
4.27/1.93	
4.27/1.93	(1) CToIRSProof (EQUIVALENT)
4.27/1.93	Parsed C Integer Program as IRS.
4.27/1.93	----------------------------------------
4.27/1.93	
4.27/1.93	(2)
4.27/1.93	Obligation:
4.27/1.93	Rules:
4.27/1.93	f1(x, oldx) -> f2(x_1, oldx) :|: TRUE
4.27/1.93	f3(x1, x2) -> f4(x1, x1) :|: TRUE
4.27/1.93	f4(x3, x4) -> f5(x5, x4) :|: TRUE
4.27/1.93	f2(x6, x7) -> f3(x6, x7) :|: x6 > 1 && 0 - 2 * x6 = x7
4.27/1.93	f5(x8, x9) -> f2(x8, x9) :|: TRUE
4.27/1.93	f2(x10, x11) -> f6(x10, x11) :|: x10 <= 1
4.27/1.94	f2(x12, x13) -> f6(x12, x13) :|: 0 - 2 * x12 < x13
4.27/1.94	f2(x14, x15) -> f6(x14, x15) :|: 0 - 2 * x14 > x15
4.27/1.94	Start term: f1(x, oldx)
4.27/1.94	
4.27/1.94	----------------------------------------
4.27/1.94	
4.27/1.94	(3) TerminationGraphProcessor (SOUND)
4.27/1.94	Constructed the termination graph and obtained one non-trivial SCC.
4.27/1.94	
4.27/1.94	----------------------------------------
4.27/1.94	
4.27/1.94	(4)
4.27/1.94	Obligation:
4.27/1.94	Rules:
4.27/1.94	f2(x6, x7) -> f3(x6, x7) :|: x6 > 1 && 0 - 2 * x6 = x7
4.27/1.94	f5(x8, x9) -> f2(x8, x9) :|: TRUE
4.27/1.94	f4(x3, x4) -> f5(x5, x4) :|: TRUE
4.27/1.94	f3(x1, x2) -> f4(x1, x1) :|: TRUE
4.27/1.94	
4.27/1.94	----------------------------------------
4.27/1.94	
4.27/1.94	(5) IntTRSCompressionProof (EQUIVALENT)
4.27/1.94	Compressed rules.
4.27/1.94	----------------------------------------
4.27/1.94	
4.27/1.94	(6)
4.27/1.94	Obligation:
4.27/1.94	Rules:
4.27/1.94	f4(x, x1) -> f4(x2, x2) :|: x2 > 1 && x1 = 0 - 2 * x2
4.27/1.94	
4.27/1.94	----------------------------------------
4.27/1.94	
4.27/1.94	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.27/1.94	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.27/1.94	
4.27/1.94	   f4(x1, x2) -> f4(x2)
4.27/1.94	
4.27/1.94	----------------------------------------
4.27/1.94	
4.27/1.94	(8)
4.27/1.94	Obligation:
4.27/1.94	Rules:
4.27/1.94	f4(x1) -> f4(x2) :|: x2 > 1 && x1 = 0 - 2 * x2
4.27/1.94	
4.27/1.94	----------------------------------------
4.27/1.94	
4.27/1.94	(9) PolynomialOrderProcessor (EQUIVALENT)
4.27/1.94	Found the following polynomial interpretation:
4.27/1.94	[f4(x)] = -x
4.27/1.94	
4.27/1.94	The following rules are decreasing:
4.27/1.94	f4(x1) -> f4(x2) :|: x2 > 1 && x1 = 0 - 2 * x2
4.27/1.94	The following rules are bounded:
4.27/1.94	f4(x1) -> f4(x2) :|: x2 > 1 && x1 = 0 - 2 * x2
4.27/1.94	
4.27/1.94	----------------------------------------
4.27/1.94	
4.27/1.94	(10)
4.27/1.94	YES
4.56/1.95	EOF