5.95/2.41	YES
6.60/2.42	proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
6.60/2.42	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.60/2.42	
6.60/2.42	
6.60/2.42	Termination of the given C Problem could be proven:
6.60/2.42	
6.60/2.42	(0) C Problem
6.60/2.42	(1) CToIRSProof [EQUIVALENT, 0 ms]
6.60/2.42	(2) IntTRS
6.60/2.42	(3) TerminationGraphProcessor [SOUND, 68 ms]
6.60/2.42	(4) IntTRS
6.60/2.42	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.60/2.42	(6) IntTRS
6.60/2.42	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
6.60/2.42	(8) IntTRS
6.60/2.42	(9) PolynomialOrderProcessor [EQUIVALENT, 16 ms]
6.60/2.42	(10) IntTRS
6.60/2.42	(11) PolynomialOrderProcessor [EQUIVALENT, 3 ms]
6.60/2.42	(12) YES
6.60/2.42	
6.60/2.42	
6.60/2.42	----------------------------------------
6.60/2.42	
6.60/2.42	(0)
6.60/2.42	Obligation:
6.60/2.42	c file /export/starexec/sandbox2/benchmark/theBenchmark.c
6.60/2.42	----------------------------------------
6.60/2.42	
6.60/2.42	(1) CToIRSProof (EQUIVALENT)
6.60/2.42	Parsed C Integer Program as IRS.
6.60/2.42	----------------------------------------
6.60/2.42	
6.60/2.42	(2)
6.60/2.42	Obligation:
6.60/2.42	Rules:
6.60/2.42	f1(c, x, y) -> f2(c, x_1, y) :|: TRUE
6.60/2.42	f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE
6.60/2.42	f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE
6.60/2.42	f6(x8, x9, x10) -> f7(x8, x9, arith) :|: TRUE && arith = x10 - 1
6.60/2.42	f7(x38, x39, x40) -> f8(x41, x39, x40) :|: TRUE && x41 = x38 + 1
6.60/2.42	f5(x14, x15, x16) -> f6(x14, x15, x16) :|: x16 > 0
6.60/2.42	f8(x17, x18, x19) -> f5(x17, x18, x19) :|: TRUE
6.60/2.42	f5(x20, x21, x22) -> f9(x20, x21, x22) :|: x22 <= 0
6.60/2.42	f9(x42, x43, x44) -> f10(x42, x45, x44) :|: TRUE && x45 = x43 - 1
6.60/2.42	f10(x46, x47, x48) -> f11(x49, x47, x48) :|: TRUE && x49 = x46 + 1
6.60/2.42	f4(x29, x30, x31) -> f5(x29, x30, x31) :|: x30 > 0
6.60/2.42	f11(x32, x33, x34) -> f4(x32, x33, x34) :|: TRUE
6.60/2.42	f4(x35, x36, x37) -> f12(x35, x36, x37) :|: x36 <= 0
6.60/2.42	Start term: f1(c, x, y)
6.60/2.42	
6.60/2.42	----------------------------------------
6.60/2.42	
6.60/2.42	(3) TerminationGraphProcessor (SOUND)
6.60/2.42	Constructed the termination graph and obtained one non-trivial SCC.
6.60/2.42	
6.60/2.42	----------------------------------------
6.60/2.42	
6.60/2.42	(4)
6.60/2.42	Obligation:
6.60/2.42	Rules:
6.60/2.42	f4(x29, x30, x31) -> f5(x29, x30, x31) :|: x30 > 0
6.60/2.42	f11(x32, x33, x34) -> f4(x32, x33, x34) :|: TRUE
6.60/2.42	f10(x46, x47, x48) -> f11(x49, x47, x48) :|: TRUE && x49 = x46 + 1
6.60/2.42	f9(x42, x43, x44) -> f10(x42, x45, x44) :|: TRUE && x45 = x43 - 1
6.60/2.42	f5(x20, x21, x22) -> f9(x20, x21, x22) :|: x22 <= 0
6.60/2.42	f8(x17, x18, x19) -> f5(x17, x18, x19) :|: TRUE
6.60/2.42	f7(x38, x39, x40) -> f8(x41, x39, x40) :|: TRUE && x41 = x38 + 1
6.60/2.42	f6(x8, x9, x10) -> f7(x8, x9, arith) :|: TRUE && arith = x10 - 1
6.60/2.42	f5(x14, x15, x16) -> f6(x14, x15, x16) :|: x16 > 0
6.60/2.42	
6.60/2.42	----------------------------------------
6.60/2.42	
6.60/2.42	(5) IntTRSCompressionProof (EQUIVALENT)
6.60/2.42	Compressed rules.
6.60/2.42	----------------------------------------
6.60/2.42	
6.60/2.42	(6)
6.60/2.42	Obligation:
6.60/2.42	Rules:
6.60/2.42	f5(x14:0, x15:0, x16:0) -> f5(x14:0 + 1, x15:0, x16:0 - 1) :|: x16:0 > 0
6.60/2.42	f5(x20:0, x21:0, x22:0) -> f5(x20:0 + 1, x21:0 - 1, x22:0) :|: x22:0 < 1 && x21:0 > 1
6.60/2.42	
6.60/2.42	----------------------------------------
6.60/2.42	
6.60/2.42	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
6.60/2.42	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
6.60/2.42	
6.60/2.42	   f5(x1, x2, x3) -> f5(x2, x3)
6.60/2.42	
6.60/2.42	----------------------------------------
6.60/2.42	
6.60/2.42	(8)
6.60/2.42	Obligation:
6.60/2.42	Rules:
6.60/2.42	f5(x15:0, x16:0) -> f5(x15:0, x16:0 - 1) :|: x16:0 > 0
6.60/2.42	f5(x21:0, x22:0) -> f5(x21:0 - 1, x22:0) :|: x22:0 < 1 && x21:0 > 1
6.60/2.42	
6.60/2.42	----------------------------------------
6.60/2.42	
6.60/2.42	(9) PolynomialOrderProcessor (EQUIVALENT)
6.60/2.42	Found the following polynomial interpretation:
6.60/2.42	[f5(x, x1)] = x1^2
6.60/2.42	
6.60/2.42	The following rules are decreasing:
6.60/2.42	f5(x15:0, x16:0) -> f5(x15:0, x16:0 - 1) :|: x16:0 > 0
6.60/2.42	The following rules are bounded:
6.60/2.42	f5(x15:0, x16:0) -> f5(x15:0, x16:0 - 1) :|: x16:0 > 0
6.60/2.42	f5(x21:0, x22:0) -> f5(x21:0 - 1, x22:0) :|: x22:0 < 1 && x21:0 > 1
6.60/2.42	
6.60/2.42	----------------------------------------
6.60/2.42	
6.60/2.42	(10)
6.60/2.42	Obligation:
6.60/2.42	Rules:
6.60/2.42	f5(x21:0, x22:0) -> f5(x21:0 - 1, x22:0) :|: x22:0 < 1 && x21:0 > 1
6.60/2.42	
6.60/2.42	----------------------------------------
6.60/2.42	
6.60/2.42	(11) PolynomialOrderProcessor (EQUIVALENT)
6.60/2.42	Found the following polynomial interpretation:
6.60/2.42	[f5(x, x1)] = x
6.60/2.42	
6.60/2.42	The following rules are decreasing:
6.60/2.42	f5(x21:0, x22:0) -> f5(x21:0 - 1, x22:0) :|: x22:0 < 1 && x21:0 > 1
6.60/2.42	The following rules are bounded:
6.60/2.42	f5(x21:0, x22:0) -> f5(x21:0 - 1, x22:0) :|: x22:0 < 1 && x21:0 > 1
6.60/2.42	
6.60/2.42	----------------------------------------
6.60/2.42	
6.60/2.42	(12)
6.60/2.42	YES
6.71/2.51	EOF