6.15/2.32	YES
6.15/2.33	proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
6.15/2.33	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.15/2.33	
6.15/2.33	
6.15/2.33	Termination of the given C Problem could be proven:
6.15/2.33	
6.15/2.33	(0) C Problem
6.15/2.33	(1) CToIRSProof [EQUIVALENT, 0 ms]
6.15/2.33	(2) IntTRS
6.15/2.33	(3) TerminationGraphProcessor [SOUND, 67 ms]
6.15/2.33	(4) IntTRS
6.15/2.33	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.15/2.33	(6) IntTRS
6.15/2.33	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
6.15/2.33	(8) IntTRS
6.15/2.33	(9) PolynomialOrderProcessor [EQUIVALENT, 11 ms]
6.15/2.33	(10) IntTRS
6.15/2.33	(11) TerminationGraphProcessor [EQUIVALENT, 3 ms]
6.15/2.33	(12) YES
6.15/2.33	
6.15/2.33	
6.15/2.33	----------------------------------------
6.15/2.33	
6.15/2.33	(0)
6.15/2.33	Obligation:
6.15/2.33	c file /export/starexec/sandbox2/benchmark/theBenchmark.c
6.15/2.33	----------------------------------------
6.15/2.33	
6.15/2.33	(1) CToIRSProof (EQUIVALENT)
6.15/2.33	Parsed C Integer Program as IRS.
6.15/2.33	----------------------------------------
6.15/2.33	
6.15/2.33	(2)
6.15/2.33	Obligation:
6.15/2.33	Rules:
6.15/2.33	f1(c, x, y) -> f2(c, x_1, y) :|: TRUE
6.15/2.33	f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE
6.15/2.33	f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE
6.15/2.33	f6(x8, x9, x10) -> f9(x8, arith, x10) :|: TRUE && arith = x9 - 1
6.15/2.33	f10(x50, x51, x52) -> f13(x50, x51, x53) :|: TRUE && x53 = x52 - 1
6.15/2.33	f7(x14, x15, x16) -> f10(x14, x15, x16) :|: x16 > 0
6.15/2.33	f7(x17, x18, x19) -> f11(x17, x18, x19) :|: x19 <= 0
6.15/2.33	f13(x20, x21, x22) -> f12(x20, x21, x22) :|: TRUE
6.15/2.33	f11(x23, x24, x25) -> f12(x23, x24, x25) :|: TRUE
6.15/2.33	f5(x26, x27, x28) -> f6(x26, x27, x28) :|: x27 > 0
6.15/2.33	f5(x29, x30, x31) -> f7(x29, x30, x31) :|: x30 <= 0
6.15/2.33	f9(x32, x33, x34) -> f8(x32, x33, x34) :|: TRUE
6.15/2.33	f12(x35, x36, x37) -> f8(x35, x36, x37) :|: TRUE
6.15/2.33	f8(x54, x55, x56) -> f14(x57, x55, x56) :|: TRUE && x57 = x54 + 1
6.15/2.33	f4(x41, x42, x43) -> f5(x41, x42, x43) :|: x42 + x43 > 0
6.15/2.33	f14(x44, x45, x46) -> f4(x44, x45, x46) :|: TRUE
6.15/2.33	f4(x47, x48, x49) -> f15(x47, x48, x49) :|: x48 + x49 <= 0
6.15/2.33	Start term: f1(c, x, y)
6.15/2.33	
6.15/2.33	----------------------------------------
6.15/2.33	
6.15/2.33	(3) TerminationGraphProcessor (SOUND)
6.15/2.33	Constructed the termination graph and obtained one non-trivial SCC.
6.15/2.33	
6.15/2.33	----------------------------------------
6.15/2.33	
6.15/2.33	(4)
6.15/2.33	Obligation:
6.15/2.33	Rules:
6.15/2.33	f4(x41, x42, x43) -> f5(x41, x42, x43) :|: x42 + x43 > 0
6.15/2.33	f14(x44, x45, x46) -> f4(x44, x45, x46) :|: TRUE
6.15/2.33	f8(x54, x55, x56) -> f14(x57, x55, x56) :|: TRUE && x57 = x54 + 1
6.15/2.33	f9(x32, x33, x34) -> f8(x32, x33, x34) :|: TRUE
6.15/2.33	f6(x8, x9, x10) -> f9(x8, arith, x10) :|: TRUE && arith = x9 - 1
6.15/2.33	f5(x26, x27, x28) -> f6(x26, x27, x28) :|: x27 > 0
6.15/2.33	f12(x35, x36, x37) -> f8(x35, x36, x37) :|: TRUE
6.15/2.33	f13(x20, x21, x22) -> f12(x20, x21, x22) :|: TRUE
6.15/2.33	f10(x50, x51, x52) -> f13(x50, x51, x53) :|: TRUE && x53 = x52 - 1
6.15/2.33	f7(x14, x15, x16) -> f10(x14, x15, x16) :|: x16 > 0
6.15/2.33	f5(x29, x30, x31) -> f7(x29, x30, x31) :|: x30 <= 0
6.15/2.33	f11(x23, x24, x25) -> f12(x23, x24, x25) :|: TRUE
6.15/2.33	f7(x17, x18, x19) -> f11(x17, x18, x19) :|: x19 <= 0
6.15/2.33	
6.15/2.33	----------------------------------------
6.15/2.33	
6.15/2.33	(5) IntTRSCompressionProof (EQUIVALENT)
6.15/2.33	Compressed rules.
6.15/2.33	----------------------------------------
6.15/2.33	
6.15/2.33	(6)
6.15/2.33	Obligation:
6.15/2.33	Rules:
6.15/2.33	f8(x54:0, x55:0, x56:0) -> f8(x54:0 + 1, x55:0, x56:0) :|: x55:0 + x56:0 > 0 && x55:0 < 1 && x56:0 < 1
6.15/2.33	f8(x, x1, x2) -> f8(x + 1, x1, x2 - 1) :|: x1 + x2 > 0 && x1 < 1 && x2 > 0
6.15/2.33	f8(x3, x4, x5) -> f8(x3 + 1, x4 - 1, x5) :|: x4 + x5 > 0 && x4 > 0
6.15/2.33	
6.15/2.33	----------------------------------------
6.15/2.33	
6.15/2.33	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
6.15/2.33	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
6.15/2.33	
6.15/2.33	   f8(x1, x2, x3) -> f8(x2, x3)
6.15/2.33	
6.15/2.33	----------------------------------------
6.15/2.33	
6.15/2.33	(8)
6.15/2.33	Obligation:
6.15/2.33	Rules:
6.15/2.33	f8(x55:0, x56:0) -> f8(x55:0, x56:0) :|: x55:0 + x56:0 > 0 && x55:0 < 1 && x56:0 < 1
6.15/2.33	f8(x1, x2) -> f8(x1, x2 - 1) :|: x1 + x2 > 0 && x1 < 1 && x2 > 0
6.15/2.33	f8(x4, x5) -> f8(x4 - 1, x5) :|: x4 + x5 > 0 && x4 > 0
6.15/2.33	
6.15/2.33	----------------------------------------
6.15/2.33	
6.15/2.33	(9) PolynomialOrderProcessor (EQUIVALENT)
6.15/2.33	Found the following polynomial interpretation:
6.15/2.33	[f8(x, x1)] = x + x1
6.15/2.33	
6.15/2.33	The following rules are decreasing:
6.15/2.33	f8(x1, x2) -> f8(x1, x2 - 1) :|: x1 + x2 > 0 && x1 < 1 && x2 > 0
6.15/2.33	f8(x4, x5) -> f8(x4 - 1, x5) :|: x4 + x5 > 0 && x4 > 0
6.15/2.33	The following rules are bounded:
6.15/2.33	f8(x55:0, x56:0) -> f8(x55:0, x56:0) :|: x55:0 + x56:0 > 0 && x55:0 < 1 && x56:0 < 1
6.15/2.33	f8(x1, x2) -> f8(x1, x2 - 1) :|: x1 + x2 > 0 && x1 < 1 && x2 > 0
6.15/2.33	f8(x4, x5) -> f8(x4 - 1, x5) :|: x4 + x5 > 0 && x4 > 0
6.15/2.33	
6.15/2.33	----------------------------------------
6.15/2.33	
6.15/2.33	(10)
6.15/2.33	Obligation:
6.15/2.33	Rules:
6.15/2.33	f8(x55:0, x56:0) -> f8(x55:0, x56:0) :|: x55:0 + x56:0 > 0 && x55:0 < 1 && x56:0 < 1
6.15/2.33	
6.15/2.33	----------------------------------------
6.15/2.33	
6.15/2.33	(11) TerminationGraphProcessor (EQUIVALENT)
6.15/2.33	Constructed the termination graph and obtained no non-trivial SCC(s).
6.15/2.33	
6.15/2.33	----------------------------------------
6.15/2.33	
6.15/2.33	(12)
6.15/2.33	YES
6.15/2.37	EOF