5.47/2.21	YES
5.47/2.22	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
5.47/2.22	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.47/2.22	
5.47/2.22	
5.47/2.22	Termination of the given C Problem could be proven:
5.47/2.22	
5.47/2.22	(0) C Problem
5.47/2.22	(1) CToIRSProof [EQUIVALENT, 0 ms]
5.47/2.22	(2) IntTRS
5.47/2.22	(3) TerminationGraphProcessor [SOUND, 72 ms]
5.47/2.22	(4) IntTRS
5.47/2.22	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
5.47/2.22	(6) IntTRS
5.47/2.22	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
5.47/2.22	(8) IntTRS
5.47/2.22	(9) PolynomialOrderProcessor [EQUIVALENT, 6 ms]
5.47/2.22	(10) YES
5.47/2.22	
5.47/2.22	
5.47/2.22	----------------------------------------
5.47/2.22	
5.47/2.22	(0)
5.47/2.22	Obligation:
5.47/2.22	c file /export/starexec/sandbox/benchmark/theBenchmark.c
5.47/2.22	----------------------------------------
5.47/2.22	
5.47/2.22	(1) CToIRSProof (EQUIVALENT)
5.47/2.22	Parsed C Integer Program as IRS.
5.47/2.22	----------------------------------------
5.47/2.22	
5.47/2.22	(2)
5.47/2.22	Obligation:
5.47/2.22	Rules:
5.47/2.22	f1(c, i, j, k, tmp) -> f2(c, x_1, j, k, tmp) :|: TRUE
5.47/2.22	f2(x, x1, x2, x3, x4) -> f3(x, x1, x5, x3, x4) :|: TRUE
5.47/2.22	f3(x6, x7, x8, x9, x10) -> f4(x6, x7, x8, x11, x10) :|: TRUE
5.47/2.22	f4(x12, x13, x14, x15, x16) -> f5(x12, x13, x14, x15, x17) :|: TRUE
5.47/2.22	f5(x18, x19, x20, x21, x22) -> f6(0, x19, x20, x21, x22) :|: TRUE
5.47/2.22	f7(x23, x24, x25, x26, x27) -> f8(x23, x24, x25, x26, x24) :|: TRUE
5.47/2.22	f8(x28, x29, x30, x31, x32) -> f9(x28, x30, x30, x31, x32) :|: TRUE
5.47/2.22	f9(x33, x34, x35, x36, x37) -> f10(x33, x34, arith, x36, x37) :|: TRUE && arith = x37 + 1
5.47/2.22	f10(x63, x64, x65, x66, x67) -> f11(x63, x64, x65, x68, x67) :|: TRUE && x68 = x66 - 1
5.47/2.22	f11(x69, x70, x71, x72, x73) -> f12(x74, x70, x71, x72, x73) :|: TRUE && x74 = x69 + 1
5.47/2.22	f6(x48, x49, x50, x51, x52) -> f7(x48, x49, x50, x51, x52) :|: x49 <= 100 && x50 <= x51
5.47/2.22	f12(x53, x54, x55, x56, x57) -> f6(x53, x54, x55, x56, x57) :|: TRUE
5.47/2.22	f6(x58, x59, x60, x61, x62) -> f13(x58, x59, x60, x61, x62) :|: x59 > 100
5.47/2.22	f6(x75, x76, x77, x78, x79) -> f13(x75, x76, x77, x78, x79) :|: x77 > x78
5.47/2.22	Start term: f1(c, i, j, k, tmp)
5.47/2.22	
5.47/2.22	----------------------------------------
5.47/2.22	
5.47/2.22	(3) TerminationGraphProcessor (SOUND)
5.47/2.22	Constructed the termination graph and obtained one non-trivial SCC.
5.47/2.22	
5.47/2.22	----------------------------------------
5.47/2.22	
5.47/2.22	(4)
5.47/2.22	Obligation:
5.47/2.22	Rules:
5.47/2.22	f6(x48, x49, x50, x51, x52) -> f7(x48, x49, x50, x51, x52) :|: x49 <= 100 && x50 <= x51
5.47/2.22	f12(x53, x54, x55, x56, x57) -> f6(x53, x54, x55, x56, x57) :|: TRUE
5.47/2.22	f11(x69, x70, x71, x72, x73) -> f12(x74, x70, x71, x72, x73) :|: TRUE && x74 = x69 + 1
5.47/2.22	f10(x63, x64, x65, x66, x67) -> f11(x63, x64, x65, x68, x67) :|: TRUE && x68 = x66 - 1
5.47/2.22	f9(x33, x34, x35, x36, x37) -> f10(x33, x34, arith, x36, x37) :|: TRUE && arith = x37 + 1
5.47/2.22	f8(x28, x29, x30, x31, x32) -> f9(x28, x30, x30, x31, x32) :|: TRUE
5.47/2.22	f7(x23, x24, x25, x26, x27) -> f8(x23, x24, x25, x26, x24) :|: TRUE
5.47/2.22	
5.47/2.22	----------------------------------------
5.47/2.22	
5.47/2.22	(5) IntTRSCompressionProof (EQUIVALENT)
5.47/2.22	Compressed rules.
5.47/2.22	----------------------------------------
5.47/2.22	
5.47/2.22	(6)
5.47/2.22	Obligation:
5.47/2.22	Rules:
5.47/2.22	f8(x28:0, x29:0, x30:0, x31:0, x32:0) -> f8(x28:0 + 1, x30:0, x32:0 + 1, x31:0 - 1, x30:0) :|: x30:0 < 101 && x32:0 + 1 <= x31:0 - 1
5.47/2.22	
5.47/2.22	----------------------------------------
5.47/2.22	
5.47/2.22	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
5.47/2.22	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
5.47/2.22	
5.47/2.22	   f8(x1, x2, x3, x4, x5) -> f8(x3, x4, x5)
5.47/2.22	
5.47/2.22	----------------------------------------
5.47/2.22	
5.47/2.22	(8)
5.47/2.22	Obligation:
5.47/2.22	Rules:
5.47/2.22	f8(x30:0, x31:0, x32:0) -> f8(x32:0 + 1, x31:0 - 1, x30:0) :|: x30:0 < 101 && x32:0 + 1 <= x31:0 - 1
5.47/2.22	
5.47/2.22	----------------------------------------
5.47/2.22	
5.47/2.22	(9) PolynomialOrderProcessor (EQUIVALENT)
5.47/2.22	Found the following polynomial interpretation:
5.47/2.22	[f8(x, x1, x2)] = 98 - x + x1 - x2
5.47/2.22	
5.47/2.22	The following rules are decreasing:
5.47/2.22	f8(x30:0, x31:0, x32:0) -> f8(x32:0 + 1, x31:0 - 1, x30:0) :|: x30:0 < 101 && x32:0 + 1 <= x31:0 - 1
5.47/2.22	The following rules are bounded:
5.47/2.22	f8(x30:0, x31:0, x32:0) -> f8(x32:0 + 1, x31:0 - 1, x30:0) :|: x30:0 < 101 && x32:0 + 1 <= x31:0 - 1
5.47/2.22	
5.47/2.22	----------------------------------------
5.47/2.22	
5.47/2.22	(10)
5.47/2.22	YES
5.83/2.25	EOF