4.26/1.89	YES
4.26/1.90	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.26/1.90	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.26/1.90	
4.26/1.90	
4.26/1.90	Termination of the given C Problem could be proven:
4.26/1.90	
4.26/1.90	(0) C Problem
4.26/1.90	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.26/1.90	(2) IntTRS
4.26/1.90	(3) TerminationGraphProcessor [SOUND, 49 ms]
4.26/1.90	(4) IntTRS
4.26/1.90	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
4.26/1.90	(6) IntTRS
4.26/1.90	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.26/1.90	(8) IntTRS
4.26/1.90	(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
4.26/1.90	(10) YES
4.26/1.90	
4.26/1.90	
4.26/1.90	----------------------------------------
4.26/1.90	
4.26/1.90	(0)
4.26/1.90	Obligation:
4.26/1.90	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.26/1.90	----------------------------------------
4.26/1.90	
4.26/1.90	(1) CToIRSProof (EQUIVALENT)
4.26/1.90	Parsed C Integer Program as IRS.
4.26/1.90	----------------------------------------
4.26/1.90	
4.26/1.90	(2)
4.26/1.90	Obligation:
4.26/1.90	Rules:
4.26/1.90	f1(x, y, z, res) -> f2(x_1, y, z, res) :|: TRUE
4.26/1.90	f2(x1, x2, x3, x4) -> f3(x1, x5, x3, x4) :|: TRUE
4.26/1.90	f3(x6, x7, x8, x9) -> f4(x6, x7, x8, 0) :|: TRUE
4.26/1.90	f5(x10, x11, x12, x13) -> f6(x10, x11, x10, x13) :|: TRUE
4.26/1.90	f6(x14, x15, x16, x17) -> f7(arith, x15, x16, x17) :|: TRUE && arith = x15 - 1
4.26/1.90	f7(x18, x19, x20, x21) -> f8(x18, x20, x20, x21) :|: TRUE
4.26/1.90	f8(x42, x43, x44, x45) -> f9(x42, x43, x44, x46) :|: TRUE && x46 = x45 + 1
4.26/1.90	f4(x26, x27, x28, x29) -> f5(x26, x27, x28, x29) :|: x27 > 0
4.26/1.90	f9(x30, x31, x32, x33) -> f4(x30, x31, x32, x33) :|: TRUE
4.26/1.90	f4(x34, x35, x36, x37) -> f10(x34, x35, x36, x37) :|: x35 <= 0
4.26/1.90	f10(x47, x48, x49, x50) -> f11(x47, x48, x49, x51) :|: TRUE && x51 = x50 + x47
4.26/1.90	Start term: f1(x, y, z, res)
4.26/1.90	
4.26/1.90	----------------------------------------
4.26/1.90	
4.26/1.90	(3) TerminationGraphProcessor (SOUND)
4.26/1.90	Constructed the termination graph and obtained one non-trivial SCC.
4.26/1.90	
4.26/1.90	----------------------------------------
4.26/1.90	
4.26/1.90	(4)
4.26/1.90	Obligation:
4.26/1.90	Rules:
4.26/1.90	f4(x26, x27, x28, x29) -> f5(x26, x27, x28, x29) :|: x27 > 0
4.26/1.90	f9(x30, x31, x32, x33) -> f4(x30, x31, x32, x33) :|: TRUE
4.26/1.90	f8(x42, x43, x44, x45) -> f9(x42, x43, x44, x46) :|: TRUE && x46 = x45 + 1
4.26/1.90	f7(x18, x19, x20, x21) -> f8(x18, x20, x20, x21) :|: TRUE
4.26/1.90	f6(x14, x15, x16, x17) -> f7(arith, x15, x16, x17) :|: TRUE && arith = x15 - 1
4.26/1.90	f5(x10, x11, x12, x13) -> f6(x10, x11, x10, x13) :|: TRUE
4.26/1.90	
4.26/1.90	----------------------------------------
4.26/1.90	
4.26/1.90	(5) IntTRSCompressionProof (EQUIVALENT)
4.26/1.90	Compressed rules.
4.26/1.90	----------------------------------------
4.26/1.90	
4.26/1.90	(6)
4.26/1.90	Obligation:
4.26/1.90	Rules:
4.26/1.90	f6(x14:0, x15:0, x16:0, x17:0) -> f6(x15:0 - 1, x16:0, x15:0 - 1, x17:0 + 1) :|: x16:0 > 0
4.26/1.90	
4.26/1.90	----------------------------------------
4.26/1.90	
4.26/1.90	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.26/1.90	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.26/1.90	
4.26/1.90	   f6(x1, x2, x3, x4) -> f6(x2, x3)
4.26/1.90	
4.26/1.90	----------------------------------------
4.26/1.90	
4.26/1.90	(8)
4.26/1.90	Obligation:
4.26/1.90	Rules:
4.26/1.90	f6(x15:0, x16:0) -> f6(x16:0, x15:0 - 1) :|: x16:0 > 0
4.26/1.90	
4.26/1.90	----------------------------------------
4.26/1.90	
4.26/1.90	(9) PolynomialOrderProcessor (EQUIVALENT)
4.26/1.90	Found the following polynomial interpretation:
4.26/1.90	[f6(x, x1)] = -2 + x^2 + 2*x1 + x1^2
4.26/1.90	
4.26/1.90	The following rules are decreasing:
4.26/1.90	f6(x15:0, x16:0) -> f6(x16:0, x15:0 - 1) :|: x16:0 > 0
4.26/1.90	The following rules are bounded:
4.26/1.90	f6(x15:0, x16:0) -> f6(x16:0, x15:0 - 1) :|: x16:0 > 0
4.26/1.90	
4.26/1.90	----------------------------------------
4.26/1.90	
4.26/1.90	(10)
4.26/1.90	YES
4.61/1.93	EOF