4.45/1.94	YES
4.45/1.96	proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
4.45/1.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.45/1.96	
4.45/1.96	
4.45/1.96	Termination of the given C Problem could be proven:
4.45/1.96	
4.45/1.96	(0) C Problem
4.45/1.96	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.45/1.96	(2) IntTRS
4.45/1.96	(3) TerminationGraphProcessor [SOUND, 50 ms]
4.45/1.96	(4) IntTRS
4.45/1.96	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
4.45/1.96	(6) IntTRS
4.45/1.96	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.45/1.96	(8) IntTRS
4.45/1.96	(9) PolynomialOrderProcessor [EQUIVALENT, 1 ms]
4.45/1.96	(10) YES
4.45/1.96	
4.45/1.96	
4.45/1.96	----------------------------------------
4.45/1.96	
4.45/1.96	(0)
4.45/1.96	Obligation:
4.45/1.96	c file /export/starexec/sandbox2/benchmark/theBenchmark.c
4.45/1.96	----------------------------------------
4.45/1.96	
4.45/1.96	(1) CToIRSProof (EQUIVALENT)
4.45/1.96	Parsed C Integer Program as IRS.
4.45/1.96	----------------------------------------
4.45/1.96	
4.45/1.96	(2)
4.45/1.96	Obligation:
4.45/1.96	Rules:
4.45/1.96	f1(x, y, res) -> f2(x_1, y, res) :|: TRUE
4.45/1.96	f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
4.45/1.96	f3(x5, x6, x7) -> f4(x5, x6, 0) :|: TRUE
4.45/1.96	f5(x8, x9, x10) -> f6(arith, x9, x10) :|: TRUE && arith = x8 - x9
4.45/1.96	f6(x23, x24, x25) -> f7(x23, x24, x26) :|: TRUE && x26 = x25 + 1
4.45/1.96	f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x14 >= x15 && x15 > 0
4.45/1.96	f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE
4.45/1.96	f4(x20, x21, x22) -> f8(x20, x21, x22) :|: x20 < x21
4.45/1.96	f4(x27, x28, x29) -> f8(x27, x28, x29) :|: x28 <= 0
4.45/1.96	Start term: f1(x, y, res)
4.45/1.96	
4.45/1.96	----------------------------------------
4.45/1.96	
4.45/1.96	(3) TerminationGraphProcessor (SOUND)
4.45/1.96	Constructed the termination graph and obtained one non-trivial SCC.
4.45/1.96	
4.45/1.96	----------------------------------------
4.45/1.96	
4.45/1.96	(4)
4.45/1.96	Obligation:
4.45/1.96	Rules:
4.45/1.96	f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x14 >= x15 && x15 > 0
4.45/1.96	f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE
4.45/1.96	f6(x23, x24, x25) -> f7(x23, x24, x26) :|: TRUE && x26 = x25 + 1
4.45/1.96	f5(x8, x9, x10) -> f6(arith, x9, x10) :|: TRUE && arith = x8 - x9
4.45/1.96	
4.45/1.96	----------------------------------------
4.45/1.96	
4.45/1.96	(5) IntTRSCompressionProof (EQUIVALENT)
4.45/1.96	Compressed rules.
4.45/1.96	----------------------------------------
4.45/1.96	
4.45/1.96	(6)
4.45/1.96	Obligation:
4.45/1.96	Rules:
4.45/1.96	f6(x23:0, x24:0, x25:0) -> f6(x23:0 - x24:0, x24:0, x25:0 + 1) :|: x24:0 <= x23:0 && x24:0 > 0
4.45/1.96	
4.45/1.96	----------------------------------------
4.45/1.96	
4.45/1.96	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.45/1.96	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.45/1.96	
4.45/1.96	   f6(x1, x2, x3) -> f6(x1, x2)
4.45/1.96	
4.45/1.96	----------------------------------------
4.45/1.96	
4.45/1.96	(8)
4.45/1.96	Obligation:
4.45/1.96	Rules:
4.45/1.96	f6(x23:0, x24:0) -> f6(x23:0 - x24:0, x24:0) :|: x24:0 <= x23:0 && x24:0 > 0
4.45/1.96	
4.45/1.96	----------------------------------------
4.45/1.96	
4.45/1.96	(9) PolynomialOrderProcessor (EQUIVALENT)
4.45/1.96	Found the following polynomial interpretation:
4.45/1.96	[f6(x, x1)] = x
4.45/1.96	
4.45/1.96	The following rules are decreasing:
4.45/1.96	f6(x23:0, x24:0) -> f6(x23:0 - x24:0, x24:0) :|: x24:0 <= x23:0 && x24:0 > 0
4.45/1.96	The following rules are bounded:
4.45/1.96	f6(x23:0, x24:0) -> f6(x23:0 - x24:0, x24:0) :|: x24:0 <= x23:0 && x24:0 > 0
4.45/1.96	
4.45/1.96	----------------------------------------
4.45/1.96	
4.45/1.96	(10)
4.45/1.96	YES
4.45/1.99	EOF