7.98/2.76	YES
8.03/2.77	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
8.03/2.77	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
8.03/2.77	
8.03/2.77	
8.03/2.77	Termination of the given C Problem could be proven:
8.03/2.77	
8.03/2.77	(0) C Problem
8.03/2.77	(1) CToIRSProof [EQUIVALENT, 0 ms]
8.03/2.77	(2) IntTRS
8.03/2.77	(3) TerminationGraphProcessor [SOUND, 93 ms]
8.03/2.77	(4) IntTRS
8.03/2.77	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
8.03/2.77	(6) IntTRS
8.03/2.77	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 1 ms]
8.03/2.77	(8) IntTRS
8.03/2.77	(9) PolynomialOrderProcessor [EQUIVALENT, 5 ms]
8.03/2.77	(10) YES
8.03/2.77	
8.03/2.77	
8.03/2.77	----------------------------------------
8.03/2.77	
8.03/2.77	(0)
8.03/2.77	Obligation:
8.03/2.77	c file /export/starexec/sandbox/benchmark/theBenchmark.c
8.03/2.77	----------------------------------------
8.03/2.77	
8.03/2.77	(1) CToIRSProof (EQUIVALENT)
8.03/2.77	Parsed C Integer Program as IRS.
8.03/2.77	----------------------------------------
8.03/2.77	
8.03/2.77	(2)
8.03/2.77	Obligation:
8.03/2.77	Rules:
8.03/2.77	f1(x, y, res, min) -> f2(x_1, y, res, min) :|: TRUE
8.03/2.77	f2(x1, x2, x3, x4) -> f3(x1, x5, x3, x4) :|: TRUE
8.03/2.77	f3(x6, x7, x8, x9) -> f4(x6, x7, 0, x9) :|: TRUE
8.03/2.77	f5(x10, x11, x12, x13) -> f8(x10, x11, x12, x10) :|: TRUE
8.03/2.77	f6(x14, x15, x16, x17) -> f9(x14, x15, x16, x15) :|: TRUE
8.03/2.77	f4(x18, x19, x20, x21) -> f5(x18, x19, x20, x21) :|: x18 < x19
8.03/2.77	f4(x22, x23, x24, x25) -> f6(x22, x23, x24, x25) :|: x22 >= x23
8.03/2.77	f8(x26, x27, x28, x29) -> f7(x26, x27, x28, x29) :|: TRUE
8.03/2.77	f9(x30, x31, x32, x33) -> f7(x30, x31, x32, x33) :|: TRUE
8.03/2.77	f10(x34, x35, x36, x37) -> f11(x34, arith, x36, x37) :|: TRUE && arith = x35 + 1
8.03/2.77	f11(x78, x79, x80, x81) -> f12(x78, x79, x82, x81) :|: TRUE && x82 = x80 + 1
8.03/2.77	f13(x42, x43, x44, x45) -> f16(x42, x43, x44, x42) :|: TRUE
8.03/2.77	f14(x46, x47, x48, x49) -> f17(x46, x47, x48, x47) :|: TRUE
8.03/2.77	f12(x50, x51, x52, x53) -> f13(x50, x51, x52, x53) :|: x50 < x51
8.03/2.77	f12(x54, x55, x56, x57) -> f14(x54, x55, x56, x57) :|: x54 >= x55
8.03/2.77	f16(x58, x59, x60, x61) -> f15(x58, x59, x60, x61) :|: TRUE
8.03/2.77	f17(x62, x63, x64, x65) -> f15(x62, x63, x64, x65) :|: TRUE
8.03/2.77	f7(x66, x67, x68, x69) -> f10(x66, x67, x68, x69) :|: x69 = x67
8.03/2.77	f15(x70, x71, x72, x73) -> f7(x70, x71, x72, x73) :|: TRUE
8.03/2.77	f7(x74, x75, x76, x77) -> f18(x74, x75, x76, x77) :|: x77 < x75
8.03/2.77	f7(x83, x84, x85, x86) -> f18(x83, x84, x85, x86) :|: x86 > x84
8.03/2.77	Start term: f1(x, y, res, min)
8.03/2.77	
8.03/2.77	----------------------------------------
8.03/2.77	
8.03/2.77	(3) TerminationGraphProcessor (SOUND)
8.03/2.77	Constructed the termination graph and obtained one non-trivial SCC.
8.03/2.77	
8.03/2.77	----------------------------------------
8.03/2.77	
8.03/2.77	(4)
8.03/2.77	Obligation:
8.03/2.77	Rules:
8.03/2.77	f7(x66, x67, x68, x69) -> f10(x66, x67, x68, x69) :|: x69 = x67
8.03/2.77	f15(x70, x71, x72, x73) -> f7(x70, x71, x72, x73) :|: TRUE
8.03/2.77	f16(x58, x59, x60, x61) -> f15(x58, x59, x60, x61) :|: TRUE
8.03/2.77	f13(x42, x43, x44, x45) -> f16(x42, x43, x44, x42) :|: TRUE
8.03/2.77	f12(x50, x51, x52, x53) -> f13(x50, x51, x52, x53) :|: x50 < x51
8.03/2.77	f11(x78, x79, x80, x81) -> f12(x78, x79, x82, x81) :|: TRUE && x82 = x80 + 1
8.03/2.77	f10(x34, x35, x36, x37) -> f11(x34, arith, x36, x37) :|: TRUE && arith = x35 + 1
8.03/2.77	f17(x62, x63, x64, x65) -> f15(x62, x63, x64, x65) :|: TRUE
8.03/2.77	f14(x46, x47, x48, x49) -> f17(x46, x47, x48, x47) :|: TRUE
8.03/2.77	f12(x54, x55, x56, x57) -> f14(x54, x55, x56, x57) :|: x54 >= x55
8.03/2.77	
8.03/2.77	----------------------------------------
8.03/2.77	
8.03/2.77	(5) IntTRSCompressionProof (EQUIVALENT)
8.03/2.77	Compressed rules.
8.03/2.77	----------------------------------------
8.03/2.77	
8.03/2.77	(6)
8.03/2.77	Obligation:
8.03/2.77	Rules:
8.03/2.77	f11(x78:0, x79:0, x80:0, x81:0) -> f11(x78:0, x79:0 + 1, x80:0 + 1, x79:0) :|: x79:0 <= x78:0
8.03/2.77	
8.03/2.77	----------------------------------------
8.03/2.77	
8.03/2.77	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
8.03/2.77	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
8.03/2.77	
8.03/2.77	   f11(x1, x2, x3, x4) -> f11(x1, x2)
8.03/2.77	
8.03/2.77	----------------------------------------
8.03/2.77	
8.03/2.77	(8)
8.03/2.77	Obligation:
8.03/2.77	Rules:
8.03/2.77	f11(x78:0, x79:0) -> f11(x78:0, x79:0 + 1) :|: x79:0 <= x78:0
8.03/2.77	
8.03/2.77	----------------------------------------
8.03/2.77	
8.03/2.77	(9) PolynomialOrderProcessor (EQUIVALENT)
8.03/2.77	Found the following polynomial interpretation:
8.03/2.77	[f11(x, x1)] = x - x1
8.03/2.77	
8.03/2.77	The following rules are decreasing:
8.03/2.77	f11(x78:0, x79:0) -> f11(x78:0, x79:0 + 1) :|: x79:0 <= x78:0
8.03/2.77	The following rules are bounded:
8.03/2.77	f11(x78:0, x79:0) -> f11(x78:0, x79:0 + 1) :|: x79:0 <= x78:0
8.03/2.77	
8.03/2.77	----------------------------------------
8.03/2.77	
8.03/2.77	(10)
8.03/2.77	YES
8.03/2.80	EOF