6.40/2.39	YES
6.40/2.40	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
6.40/2.40	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.40/2.40	
6.40/2.40	
6.40/2.40	Termination of the given C Problem could be proven:
6.40/2.40	
6.40/2.40	(0) C Problem
6.40/2.40	(1) CToIRSProof [EQUIVALENT, 0 ms]
6.40/2.40	(2) IntTRS
6.40/2.40	(3) TerminationGraphProcessor [SOUND, 58 ms]
6.40/2.40	(4) AND
6.40/2.40	    (5) IntTRS
6.40/2.40	        (6) IntTRSCompressionProof [EQUIVALENT, 12 ms]
6.40/2.40	        (7) IntTRS
6.40/2.40	        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
6.40/2.40	        (9) IntTRS
6.40/2.40	        (10) PolynomialOrderProcessor [EQUIVALENT, 9 ms]
6.40/2.40	        (11) YES
6.40/2.40	    (12) IntTRS
6.40/2.40	        (13) IntTRSCompressionProof [EQUIVALENT, 29 ms]
6.40/2.40	        (14) IntTRS
6.40/2.40	        (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
6.40/2.40	        (16) IntTRS
6.40/2.40	        (17) RankingReductionPairProof [EQUIVALENT, 0 ms]
6.40/2.40	        (18) YES
6.40/2.40	
6.40/2.40	
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(0)
6.40/2.40	Obligation:
6.40/2.40	c file /export/starexec/sandbox/benchmark/theBenchmark.c
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(1) CToIRSProof (EQUIVALENT)
6.40/2.40	Parsed C Integer Program as IRS.
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(2)
6.40/2.40	Obligation:
6.40/2.40	Rules:
6.40/2.40	f1(x, i, n, m) -> f2(x_1, i, n, m) :|: TRUE
6.40/2.40	f2(x1, x2, x3, x4) -> f3(x1, x5, x3, x4) :|: TRUE
6.40/2.40	f3(x6, x7, x8, x9) -> f4(x6, x7, x10, x9) :|: TRUE
6.40/2.40	f4(x11, x12, x13, x14) -> f5(x11, x12, x13, x15) :|: TRUE
6.40/2.40	f6(x16, x17, x18, x19) -> f7(x16, arith, x18, x19) :|: TRUE && arith = x17 + 1
6.40/2.40	f7(x56, x57, x58, x59) -> f8(x60, x57, x58, x59) :|: TRUE && x60 = x56 + 1
6.40/2.40	f5(x24, x25, x26, x27) -> f6(x24, x25, x26, x27) :|: x24 < x26
6.40/2.40	f8(x28, x29, x30, x31) -> f5(x28, x29, x30, x31) :|: TRUE
6.40/2.40	f5(x32, x33, x34, x35) -> f9(x32, x33, x34, x35) :|: x32 >= x34
6.40/2.40	f10(x61, x62, x63, x64) -> f11(x61, x65, x63, x64) :|: TRUE && x65 = x62 + 1
6.40/2.40	f11(x66, x67, x68, x69) -> f12(x70, x67, x68, x69) :|: TRUE && x70 = x66 + 1
6.40/2.40	f9(x44, x45, x46, x47) -> f10(x44, x45, x46, x47) :|: x44 < x47
6.40/2.40	f12(x48, x49, x50, x51) -> f9(x48, x49, x50, x51) :|: TRUE
6.40/2.40	f9(x52, x53, x54, x55) -> f13(x52, x53, x54, x55) :|: x52 >= x55
6.40/2.40	Start term: f1(x, i, n, m)
6.40/2.40	
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(3) TerminationGraphProcessor (SOUND)
6.40/2.40	Constructed the termination graph and obtained 2 non-trivial SCCs.
6.40/2.40	
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(4)
6.40/2.40	Complex Obligation (AND)
6.40/2.40	
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(5)
6.40/2.40	Obligation:
6.40/2.40	Rules:
6.40/2.40	f5(x24, x25, x26, x27) -> f6(x24, x25, x26, x27) :|: x24 < x26
6.40/2.40	f8(x28, x29, x30, x31) -> f5(x28, x29, x30, x31) :|: TRUE
6.40/2.40	f7(x56, x57, x58, x59) -> f8(x60, x57, x58, x59) :|: TRUE && x60 = x56 + 1
6.40/2.40	f6(x16, x17, x18, x19) -> f7(x16, arith, x18, x19) :|: TRUE && arith = x17 + 1
6.40/2.40	
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(6) IntTRSCompressionProof (EQUIVALENT)
6.40/2.40	Compressed rules.
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(7)
6.40/2.40	Obligation:
6.40/2.40	Rules:
6.40/2.40	f7(x56:0, x57:0, x58:0, x59:0) -> f7(x56:0 + 1, x57:0 + 1, x58:0, x59:0) :|: x58:0 > x56:0 + 1
6.40/2.40	
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(8) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
6.40/2.40	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
6.40/2.40	
6.40/2.40	   f7(x1, x2, x3, x4) -> f7(x1, x3)
6.40/2.40	
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(9)
6.40/2.40	Obligation:
6.40/2.40	Rules:
6.40/2.40	f7(x56:0, x58:0) -> f7(x56:0 + 1, x58:0) :|: x58:0 > x56:0 + 1
6.40/2.40	
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(10) PolynomialOrderProcessor (EQUIVALENT)
6.40/2.40	Found the following polynomial interpretation:
6.40/2.40	[f7(x, x1)] = -x + x1
6.40/2.40	
6.40/2.40	The following rules are decreasing:
6.40/2.40	f7(x56:0, x58:0) -> f7(x56:0 + 1, x58:0) :|: x58:0 > x56:0 + 1
6.40/2.40	The following rules are bounded:
6.40/2.40	f7(x56:0, x58:0) -> f7(x56:0 + 1, x58:0) :|: x58:0 > x56:0 + 1
6.40/2.40	
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(11)
6.40/2.40	YES
6.40/2.40	
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(12)
6.40/2.40	Obligation:
6.40/2.40	Rules:
6.40/2.40	f9(x44, x45, x46, x47) -> f10(x44, x45, x46, x47) :|: x44 < x47
6.40/2.40	f12(x48, x49, x50, x51) -> f9(x48, x49, x50, x51) :|: TRUE
6.40/2.40	f11(x66, x67, x68, x69) -> f12(x70, x67, x68, x69) :|: TRUE && x70 = x66 + 1
6.40/2.40	f10(x61, x62, x63, x64) -> f11(x61, x65, x63, x64) :|: TRUE && x65 = x62 + 1
6.40/2.40	
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(13) IntTRSCompressionProof (EQUIVALENT)
6.40/2.40	Compressed rules.
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(14)
6.40/2.40	Obligation:
6.40/2.40	Rules:
6.40/2.40	f11(x66:0, x67:0, x68:0, x69:0) -> f11(x66:0 + 1, x67:0 + 1, x68:0, x69:0) :|: x69:0 > x66:0 + 1
6.40/2.40	
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(15) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
6.40/2.40	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
6.40/2.40	
6.40/2.40	   f11(x1, x2, x3, x4) -> f11(x1, x4)
6.40/2.40	
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(16)
6.40/2.40	Obligation:
6.40/2.40	Rules:
6.40/2.40	f11(x66:0, x69:0) -> f11(x66:0 + 1, x69:0) :|: x69:0 > x66:0 + 1
6.40/2.40	
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(17) RankingReductionPairProof (EQUIVALENT)
6.40/2.40	Interpretation:
6.40/2.40	[ f11 ] = f11_2 + -1*f11_1
6.40/2.40	
6.40/2.40	The following rules are decreasing:
6.40/2.40	f11(x66:0, x69:0) -> f11(x66:0 + 1, x69:0) :|: x69:0 > x66:0 + 1
6.40/2.40	
6.40/2.40	The following rules are bounded:
6.40/2.40	f11(x66:0, x69:0) -> f11(x66:0 + 1, x69:0) :|: x69:0 > x66:0 + 1
6.40/2.40	
6.40/2.40	
6.40/2.40	----------------------------------------
6.40/2.40	
6.40/2.40	(18)
6.40/2.40	YES
6.65/2.43	EOF