4.68/1.94	YES
4.73/1.95	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.73/1.95	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.73/1.95	
4.73/1.95	
4.73/1.95	Termination of the given C Problem could be proven:
4.73/1.95	
4.73/1.95	(0) C Problem
4.73/1.95	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.73/1.95	(2) IntTRS
4.73/1.95	(3) TerminationGraphProcessor [SOUND, 46 ms]
4.73/1.95	(4) IntTRS
4.73/1.95	(5) IntTRSCompressionProof [EQUIVALENT, 34 ms]
4.73/1.95	(6) IntTRS
4.73/1.95	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.73/1.95	(8) IntTRS
4.73/1.95	(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
4.73/1.95	(10) YES
4.73/1.95	
4.73/1.95	
4.73/1.95	----------------------------------------
4.73/1.95	
4.73/1.95	(0)
4.73/1.95	Obligation:
4.73/1.95	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.73/1.95	----------------------------------------
4.73/1.95	
4.73/1.95	(1) CToIRSProof (EQUIVALENT)
4.73/1.95	Parsed C Integer Program as IRS.
4.73/1.95	----------------------------------------
4.73/1.95	
4.73/1.95	(2)
4.73/1.95	Obligation:
4.73/1.95	Rules:
4.73/1.95	f1(x, y) -> f2(x_1, y) :|: TRUE
4.73/1.95	f2(x1, x2) -> f3(x1, x3) :|: TRUE
4.73/1.95	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 - x5
4.73/1.95	f5(x6, x7) -> f6(x6, x8) :|: TRUE
4.73/1.95	f3(x9, x10) -> f4(x9, x10) :|: x9 >= 0 && x10 >= 1
4.73/1.95	f6(x11, x12) -> f3(x11, x12) :|: TRUE
4.73/1.95	f3(x13, x14) -> f7(x13, x14) :|: x13 < 0
4.73/1.95	f3(x15, x16) -> f7(x15, x16) :|: x16 < 1
4.73/1.95	Start term: f1(x, y)
4.73/1.95	
4.73/1.95	----------------------------------------
4.73/1.95	
4.73/1.95	(3) TerminationGraphProcessor (SOUND)
4.73/1.95	Constructed the termination graph and obtained one non-trivial SCC.
4.73/1.95	
4.73/1.95	----------------------------------------
4.73/1.95	
4.73/1.95	(4)
4.73/1.95	Obligation:
4.73/1.95	Rules:
4.73/1.95	f3(x9, x10) -> f4(x9, x10) :|: x9 >= 0 && x10 >= 1
4.73/1.95	f6(x11, x12) -> f3(x11, x12) :|: TRUE
4.73/1.95	f5(x6, x7) -> f6(x6, x8) :|: TRUE
4.73/1.95	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 - x5
4.73/1.95	
4.73/1.95	----------------------------------------
4.73/1.95	
4.73/1.95	(5) IntTRSCompressionProof (EQUIVALENT)
4.73/1.95	Compressed rules.
4.73/1.95	----------------------------------------
4.73/1.95	
4.73/1.95	(6)
4.73/1.95	Obligation:
4.73/1.95	Rules:
4.73/1.95	f5(x6:0, x7:0) -> f5(x6:0 - x8:0, x8:0) :|: x6:0 > -1 && x8:0 > 0
4.73/1.95	
4.73/1.95	----------------------------------------
4.73/1.95	
4.73/1.95	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.73/1.95	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.73/1.95	
4.73/1.95	   f5(x1, x2) -> f5(x1)
4.73/1.95	
4.73/1.95	----------------------------------------
4.73/1.95	
4.73/1.95	(8)
4.73/1.95	Obligation:
4.73/1.95	Rules:
4.73/1.95	f5(x6:0) -> f5(x6:0 - x8:0) :|: x6:0 > -1 && x8:0 > 0
4.73/1.95	
4.73/1.95	----------------------------------------
4.73/1.95	
4.73/1.95	(9) PolynomialOrderProcessor (EQUIVALENT)
4.73/1.95	Found the following polynomial interpretation:
4.73/1.95	[f5(x)] = x
4.73/1.95	
4.73/1.95	The following rules are decreasing:
4.73/1.95	f5(x6:0) -> f5(x6:0 - x8:0) :|: x6:0 > -1 && x8:0 > 0
4.73/1.95	The following rules are bounded:
4.73/1.95	f5(x6:0) -> f5(x6:0 - x8:0) :|: x6:0 > -1 && x8:0 > 0
4.73/1.95	
4.73/1.95	----------------------------------------
4.73/1.95	
4.73/1.95	(10)
4.73/1.95	YES
4.73/1.97	EOF