6.73/2.58	YES
6.73/2.59	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
6.73/2.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.73/2.59	
6.73/2.59	
6.73/2.59	Termination of the given C Problem could be proven:
6.73/2.59	
6.73/2.59	(0) C Problem
6.73/2.59	(1) CToIRSProof [EQUIVALENT, 0 ms]
6.73/2.59	(2) IntTRS
6.73/2.59	(3) TerminationGraphProcessor [SOUND, 77 ms]
6.73/2.59	(4) IntTRS
6.73/2.59	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.73/2.59	(6) IntTRS
6.73/2.59	(7) PolynomialOrderProcessor [EQUIVALENT, 16 ms]
6.73/2.59	(8) IntTRS
6.73/2.59	(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
6.73/2.59	(10) YES
6.73/2.59	
6.73/2.59	
6.73/2.59	----------------------------------------
6.73/2.59	
6.73/2.59	(0)
6.73/2.59	Obligation:
6.73/2.59	c file /export/starexec/sandbox/benchmark/theBenchmark.c
6.73/2.59	----------------------------------------
6.73/2.59	
6.73/2.59	(1) CToIRSProof (EQUIVALENT)
6.73/2.59	Parsed C Integer Program as IRS.
6.73/2.59	----------------------------------------
6.73/2.59	
6.73/2.59	(2)
6.73/2.59	Obligation:
6.73/2.59	Rules:
6.73/2.59	f1(i, j, m, n) -> f2(i, j, m, x_1) :|: TRUE
6.73/2.59	f2(x, x1, x2, x3) -> f3(x, x1, x4, x3) :|: TRUE
6.73/2.59	f4(x5, x6, x7, x8) -> f7(0, x6, x7, x8) :|: TRUE
6.73/2.59	f7(x9, x10, x11, x12) -> f8(x9, 0, x11, x12) :|: TRUE
6.73/2.59	f10(x13, x14, x15, x16) -> f13(x13, arith, x15, x16) :|: TRUE && arith = x14 + 1
6.73/2.59	f11(x17, x18, x19, x20) -> f14(x17, 0, x19, x20) :|: TRUE
6.73/2.59	f14(x69, x70, x71, x72) -> f15(x73, x70, x71, x72) :|: TRUE && x73 = x69 + 1
6.73/2.59	f9(x25, x26, x27, x28) -> f10(x25, x26, x27, x28) :|: x26 < x27
6.73/2.59	f9(x29, x30, x31, x32) -> f11(x29, x30, x31, x32) :|: x30 >= x31
6.73/2.59	f13(x33, x34, x35, x36) -> f12(x33, x34, x35, x36) :|: TRUE
6.73/2.59	f15(x37, x38, x39, x40) -> f12(x37, x38, x39, x40) :|: TRUE
6.73/2.59	f8(x41, x42, x43, x44) -> f9(x41, x42, x43, x44) :|: x41 < x44
6.73/2.59	f12(x45, x46, x47, x48) -> f8(x45, x46, x47, x48) :|: TRUE
6.73/2.59	f8(x49, x50, x51, x52) -> f16(x49, x50, x51, x52) :|: x49 >= x52
6.73/2.59	f3(x53, x54, x55, x56) -> f4(x53, x54, x55, x56) :|: x55 > 0 && x56 > x55
6.73/2.59	f3(x57, x58, x59, x60) -> f5(x57, x58, x59, x60) :|: x59 <= 0
6.73/2.59	f3(x74, x75, x76, x77) -> f5(x74, x75, x76, x77) :|: x77 <= x76
6.73/2.59	f16(x61, x62, x63, x64) -> f6(x61, x62, x63, x64) :|: TRUE
6.73/2.59	f5(x65, x66, x67, x68) -> f6(x65, x66, x67, x68) :|: TRUE
6.73/2.59	Start term: f1(i, j, m, n)
6.73/2.59	
6.73/2.59	----------------------------------------
6.73/2.59	
6.73/2.59	(3) TerminationGraphProcessor (SOUND)
6.73/2.59	Constructed the termination graph and obtained one non-trivial SCC.
6.73/2.59	
6.73/2.59	----------------------------------------
6.73/2.59	
6.73/2.59	(4)
6.73/2.59	Obligation:
6.73/2.59	Rules:
6.73/2.59	f8(x41, x42, x43, x44) -> f9(x41, x42, x43, x44) :|: x41 < x44
6.73/2.59	f12(x45, x46, x47, x48) -> f8(x45, x46, x47, x48) :|: TRUE
6.73/2.59	f13(x33, x34, x35, x36) -> f12(x33, x34, x35, x36) :|: TRUE
6.73/2.59	f10(x13, x14, x15, x16) -> f13(x13, arith, x15, x16) :|: TRUE && arith = x14 + 1
6.73/2.59	f9(x25, x26, x27, x28) -> f10(x25, x26, x27, x28) :|: x26 < x27
6.73/2.59	f15(x37, x38, x39, x40) -> f12(x37, x38, x39, x40) :|: TRUE
6.73/2.59	f14(x69, x70, x71, x72) -> f15(x73, x70, x71, x72) :|: TRUE && x73 = x69 + 1
6.73/2.59	f11(x17, x18, x19, x20) -> f14(x17, 0, x19, x20) :|: TRUE
6.73/2.59	f9(x29, x30, x31, x32) -> f11(x29, x30, x31, x32) :|: x30 >= x31
6.73/2.59	
6.73/2.59	----------------------------------------
6.73/2.59	
6.73/2.59	(5) IntTRSCompressionProof (EQUIVALENT)
6.73/2.59	Compressed rules.
6.73/2.59	----------------------------------------
6.73/2.59	
6.73/2.59	(6)
6.73/2.59	Obligation:
6.73/2.59	Rules:
6.73/2.59	f12(x45:0, x46:0, x47:0, x48:0) -> f12(x45:0, x46:0 + 1, x47:0, x48:0) :|: x48:0 > x45:0 && x47:0 > x46:0
6.73/2.59	f12(x, x1, x2, x3) -> f12(x + 1, 0, x2, x3) :|: x3 > x && x2 <= x1
6.73/2.59	
6.73/2.59	----------------------------------------
6.73/2.59	
6.73/2.59	(7) PolynomialOrderProcessor (EQUIVALENT)
6.73/2.59	Found the following polynomial interpretation:
6.73/2.59	[f12(x, x1, x2, x3)] = -x + x3
6.73/2.59	
6.73/2.59	The following rules are decreasing:
6.73/2.59	f12(x, x1, x2, x3) -> f12(x + 1, 0, x2, x3) :|: x3 > x && x2 <= x1
6.73/2.59	The following rules are bounded:
6.73/2.59	f12(x45:0, x46:0, x47:0, x48:0) -> f12(x45:0, x46:0 + 1, x47:0, x48:0) :|: x48:0 > x45:0 && x47:0 > x46:0
6.73/2.59	f12(x, x1, x2, x3) -> f12(x + 1, 0, x2, x3) :|: x3 > x && x2 <= x1
6.73/2.59	
6.73/2.59	----------------------------------------
6.73/2.59	
6.73/2.59	(8)
6.73/2.59	Obligation:
6.73/2.59	Rules:
6.73/2.59	f12(x45:0, x46:0, x47:0, x48:0) -> f12(x45:0, x46:0 + 1, x47:0, x48:0) :|: x48:0 > x45:0 && x47:0 > x46:0
6.73/2.59	
6.73/2.59	----------------------------------------
6.73/2.59	
6.73/2.59	(9) PolynomialOrderProcessor (EQUIVALENT)
6.73/2.59	Found the following polynomial interpretation:
6.73/2.59	[f12(x, x1, x2, x3)] = -x1 + x2
6.73/2.59	
6.73/2.59	The following rules are decreasing:
6.73/2.59	f12(x45:0, x46:0, x47:0, x48:0) -> f12(x45:0, x46:0 + 1, x47:0, x48:0) :|: x48:0 > x45:0 && x47:0 > x46:0
6.73/2.59	The following rules are bounded:
6.73/2.59	f12(x45:0, x46:0, x47:0, x48:0) -> f12(x45:0, x46:0 + 1, x47:0, x48:0) :|: x48:0 > x45:0 && x47:0 > x46:0
6.73/2.59	
6.73/2.59	----------------------------------------
6.73/2.59	
6.73/2.59	(10)
6.73/2.59	YES
6.89/2.62	EOF