5.89/2.41	YES
6.28/2.42	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
6.28/2.42	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.28/2.42	
6.28/2.42	
6.28/2.42	Termination of the given C Problem could be proven:
6.28/2.42	
6.28/2.42	(0) C Problem
6.28/2.42	(1) CToIRSProof [EQUIVALENT, 0 ms]
6.28/2.42	(2) IntTRS
6.28/2.42	(3) TerminationGraphProcessor [SOUND, 64 ms]
6.28/2.42	(4) AND
6.28/2.42	    (5) IntTRS
6.28/2.42	        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.28/2.42	        (7) IntTRS
6.28/2.42	        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
6.28/2.42	        (9) IntTRS
6.28/2.42	        (10) RankingReductionPairProof [EQUIVALENT, 3 ms]
6.28/2.42	        (11) YES
6.28/2.42	    (12) IntTRS
6.28/2.42	        (13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.28/2.42	        (14) IntTRS
6.28/2.42	        (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
6.28/2.42	        (16) IntTRS
6.28/2.42	        (17) PolynomialOrderProcessor [EQUIVALENT, 4 ms]
6.28/2.42	        (18) YES
6.28/2.42	
6.28/2.42	
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(0)
6.28/2.42	Obligation:
6.28/2.42	c file /export/starexec/sandbox/benchmark/theBenchmark.c
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(1) CToIRSProof (EQUIVALENT)
6.28/2.42	Parsed C Integer Program as IRS.
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(2)
6.28/2.42	Obligation:
6.28/2.42	Rules:
6.28/2.42	f1(i, j, c) -> f2(i, j, 0) :|: TRUE
6.28/2.42	f2(x, x1, x2) -> f3(0, x1, x2) :|: TRUE
6.28/2.42	f4(x3, x4, x5) -> f5(x3, x4, arith) :|: TRUE && arith = x5 + 1
6.28/2.42	f5(x36, x37, x38) -> f6(x39, x37, x38) :|: TRUE && x39 = x36 + 1
6.28/2.42	f3(x9, x10, x11) -> f4(x9, x10, x11) :|: x9 < 100
6.28/2.42	f6(x12, x13, x14) -> f3(x12, x13, x14) :|: TRUE
6.28/2.42	f3(x15, x16, x17) -> f7(x15, x16, x17) :|: x15 >= 100
6.28/2.42	f7(x18, x19, x20) -> f8(x18, 5, x20) :|: TRUE
6.28/2.42	f9(x40, x41, x42) -> f10(x40, x41, x43) :|: TRUE && x43 = x42 + 1
6.28/2.42	f10(x44, x45, x46) -> f11(x44, x47, x46) :|: TRUE && x47 = x45 + 3
6.28/2.42	f8(x27, x28, x29) -> f9(x27, x28, x29) :|: x28 < 21
6.28/2.42	f11(x30, x31, x32) -> f8(x30, x31, x32) :|: TRUE
6.28/2.42	f8(x33, x34, x35) -> f12(x33, x34, x35) :|: x34 >= 21
6.28/2.42	Start term: f1(i, j, c)
6.28/2.42	
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(3) TerminationGraphProcessor (SOUND)
6.28/2.42	Constructed the termination graph and obtained 2 non-trivial SCCs.
6.28/2.42	
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(4)
6.28/2.42	Complex Obligation (AND)
6.28/2.42	
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(5)
6.28/2.42	Obligation:
6.28/2.42	Rules:
6.28/2.42	f3(x9, x10, x11) -> f4(x9, x10, x11) :|: x9 < 100
6.28/2.42	f6(x12, x13, x14) -> f3(x12, x13, x14) :|: TRUE
6.28/2.42	f5(x36, x37, x38) -> f6(x39, x37, x38) :|: TRUE && x39 = x36 + 1
6.28/2.42	f4(x3, x4, x5) -> f5(x3, x4, arith) :|: TRUE && arith = x5 + 1
6.28/2.42	
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(6) IntTRSCompressionProof (EQUIVALENT)
6.28/2.42	Compressed rules.
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(7)
6.28/2.42	Obligation:
6.28/2.42	Rules:
6.28/2.42	f5(x36:0, x37:0, x38:0) -> f5(x36:0 + 1, x37:0, x38:0 + 1) :|: x36:0 < 99
6.28/2.42	
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(8) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
6.28/2.42	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
6.28/2.42	
6.28/2.42	   f5(x1, x2, x3) -> f5(x1)
6.28/2.42	
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(9)
6.28/2.42	Obligation:
6.28/2.42	Rules:
6.28/2.42	f5(x36:0) -> f5(x36:0 + 1) :|: x36:0 < 99
6.28/2.42	
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(10) RankingReductionPairProof (EQUIVALENT)
6.28/2.42	Interpretation:
6.28/2.42	[ f5 ] = -1*f5_1
6.28/2.42	
6.28/2.42	The following rules are decreasing:
6.28/2.42	f5(x36:0) -> f5(x36:0 + 1) :|: x36:0 < 99
6.28/2.42	
6.28/2.42	The following rules are bounded:
6.28/2.42	f5(x36:0) -> f5(x36:0 + 1) :|: x36:0 < 99
6.28/2.42	
6.28/2.42	
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(11)
6.28/2.42	YES
6.28/2.42	
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(12)
6.28/2.42	Obligation:
6.28/2.42	Rules:
6.28/2.42	f8(x27, x28, x29) -> f9(x27, x28, x29) :|: x28 < 21
6.28/2.42	f11(x30, x31, x32) -> f8(x30, x31, x32) :|: TRUE
6.28/2.42	f10(x44, x45, x46) -> f11(x44, x47, x46) :|: TRUE && x47 = x45 + 3
6.28/2.42	f9(x40, x41, x42) -> f10(x40, x41, x43) :|: TRUE && x43 = x42 + 1
6.28/2.42	
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(13) IntTRSCompressionProof (EQUIVALENT)
6.28/2.42	Compressed rules.
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(14)
6.28/2.42	Obligation:
6.28/2.42	Rules:
6.28/2.42	f10(x44:0, x45:0, x46:0) -> f10(x44:0, x45:0 + 3, x46:0 + 1) :|: x45:0 < 18
6.28/2.42	
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(15) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
6.28/2.42	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
6.28/2.42	
6.28/2.42	   f10(x1, x2, x3) -> f10(x2)
6.28/2.42	
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(16)
6.28/2.42	Obligation:
6.28/2.42	Rules:
6.28/2.42	f10(x45:0) -> f10(x45:0 + 3) :|: x45:0 < 18
6.28/2.42	
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(17) PolynomialOrderProcessor (EQUIVALENT)
6.28/2.42	Found the following polynomial interpretation:
6.28/2.42	[f10(x)] = 194 - 9*x
6.28/2.42	
6.28/2.42	The following rules are decreasing:
6.28/2.42	f10(x45:0) -> f10(x45:0 + 3) :|: x45:0 < 18
6.28/2.42	The following rules are bounded:
6.28/2.42	f10(x45:0) -> f10(x45:0 + 3) :|: x45:0 < 18
6.28/2.42	
6.28/2.42	----------------------------------------
6.28/2.42	
6.28/2.42	(18)
6.28/2.42	YES
6.28/2.46	EOF