6.79/2.41	YES
6.79/2.43	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
6.79/2.43	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.79/2.43	
6.79/2.43	
6.79/2.43	Termination of the given C Problem could be proven:
6.79/2.43	
6.79/2.43	(0) C Problem
6.79/2.43	(1) CToIRSProof [EQUIVALENT, 0 ms]
6.79/2.43	(2) IntTRS
6.79/2.43	(3) TerminationGraphProcessor [SOUND, 69 ms]
6.79/2.43	(4) IntTRS
6.79/2.43	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.79/2.43	(6) IntTRS
6.79/2.43	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
6.79/2.43	(8) IntTRS
6.79/2.43	(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
6.79/2.43	(10) AND
6.79/2.43	    (11) IntTRS
6.79/2.43	        (12) TerminationGraphProcessor [EQUIVALENT, 0 ms]
6.79/2.43	        (13) YES
6.79/2.43	    (14) IntTRS
6.79/2.43	        (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
6.79/2.43	        (16) IntTRS
6.79/2.43	        (17) RankingReductionPairProof [EQUIVALENT, 4 ms]
6.79/2.43	        (18) YES
6.79/2.43	
6.79/2.43	
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(0)
6.79/2.43	Obligation:
6.79/2.43	c file /export/starexec/sandbox/benchmark/theBenchmark.c
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(1) CToIRSProof (EQUIVALENT)
6.79/2.43	Parsed C Integer Program as IRS.
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(2)
6.79/2.43	Obligation:
6.79/2.43	Rules:
6.79/2.43	f1(c, x, y) -> f2(c, x_1, y) :|: TRUE
6.79/2.43	f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE
6.79/2.43	f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE
6.79/2.43	f6(x8, x9, x10) -> f7(x8, arith, x10) :|: TRUE && arith = x9 - 1
6.79/2.43	f7(x35, x36, x37) -> f8(x35, x36, x38) :|: TRUE && x38 = x37 - 1
6.79/2.43	f8(x39, x40, x41) -> f9(x42, x40, x41) :|: TRUE && x42 = x39 + 1
6.79/2.43	f5(x17, x18, x19) -> f6(x17, x18, x19) :|: x19 > 0
6.79/2.43	f9(x20, x21, x22) -> f5(x20, x21, x22) :|: TRUE
6.79/2.43	f5(x23, x24, x25) -> f10(x23, x24, x25) :|: x25 <= 0
6.79/2.43	f4(x26, x27, x28) -> f5(x26, x27, x28) :|: x27 = x28 && x27 > 0
6.79/2.43	f10(x29, x30, x31) -> f4(x29, x30, x31) :|: TRUE
6.79/2.43	f4(x32, x33, x34) -> f11(x32, x33, x34) :|: x33 <= 0
6.79/2.43	f4(x43, x44, x45) -> f11(x43, x44, x45) :|: x44 < x45
6.79/2.43	f4(x46, x47, x48) -> f11(x46, x47, x48) :|: x47 > x48
6.79/2.43	Start term: f1(c, x, y)
6.79/2.43	
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(3) TerminationGraphProcessor (SOUND)
6.79/2.43	Constructed the termination graph and obtained one non-trivial SCC.
6.79/2.43	
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(4)
6.79/2.43	Obligation:
6.79/2.43	Rules:
6.79/2.43	f4(x26, x27, x28) -> f5(x26, x27, x28) :|: x27 = x28 && x27 > 0
6.79/2.43	f10(x29, x30, x31) -> f4(x29, x30, x31) :|: TRUE
6.79/2.43	f5(x23, x24, x25) -> f10(x23, x24, x25) :|: x25 <= 0
6.79/2.43	f9(x20, x21, x22) -> f5(x20, x21, x22) :|: TRUE
6.79/2.43	f8(x39, x40, x41) -> f9(x42, x40, x41) :|: TRUE && x42 = x39 + 1
6.79/2.43	f7(x35, x36, x37) -> f8(x35, x36, x38) :|: TRUE && x38 = x37 - 1
6.79/2.43	f6(x8, x9, x10) -> f7(x8, arith, x10) :|: TRUE && arith = x9 - 1
6.79/2.43	f5(x17, x18, x19) -> f6(x17, x18, x19) :|: x19 > 0
6.79/2.43	
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(5) IntTRSCompressionProof (EQUIVALENT)
6.79/2.43	Compressed rules.
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(6)
6.79/2.43	Obligation:
6.79/2.43	Rules:
6.79/2.43	f5(x17:0, x18:0, x19:0) -> f5(x17:0 + 1, x18:0 - 1, x19:0 - 1) :|: x19:0 > 0
6.79/2.43	f5(x23:0, x24:0, x24:01) -> f5(x23:0, x24:0, x24:0) :|: x24:0 < 1 && x24:0 > 0 && x24:0 = x24:01
6.79/2.43	
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
6.79/2.43	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
6.79/2.43	
6.79/2.43	   f5(x1, x2, x3) -> f5(x2, x3)
6.79/2.43	
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(8)
6.79/2.43	Obligation:
6.79/2.43	Rules:
6.79/2.43	f5(x18:0, x19:0) -> f5(x18:0 - 1, x19:0 - 1) :|: x19:0 > 0
6.79/2.43	f5(x24:0, x24:01) -> f5(x24:0, x24:0) :|: x24:0 < 1 && x24:0 > 0 && x24:0 = x24:01
6.79/2.43	
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(9) PolynomialOrderProcessor (EQUIVALENT)
6.79/2.43	Found the following polynomial interpretation:
6.79/2.43	[f5(x, x1)] = d + x1
6.79/2.43	
6.79/2.43	The following rules are decreasing:
6.79/2.43	f5(x18:0, x19:0) -> f5(x18:0 - 1, x19:0 - 1) :|: x19:0 > 0
6.79/2.43	The following rules are bounded:
6.79/2.43	f5(x24:0, x24:01) -> f5(x24:0, x24:0) :|: x24:0 < 1 && x24:0 > 0 && x24:0 = x24:01
6.79/2.43	
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(10)
6.79/2.43	Complex Obligation (AND)
6.79/2.43	
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(11)
6.79/2.43	Obligation:
6.79/2.43	Rules:
6.79/2.43	f5(x24:0, x24:01) -> f5(x24:0, x24:0) :|: x24:0 < 1 && x24:0 > 0 && x24:0 = x24:01
6.79/2.43	
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(12) TerminationGraphProcessor (EQUIVALENT)
6.79/2.43	Constructed the termination graph and obtained no non-trivial SCC(s).
6.79/2.43	
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(13)
6.79/2.43	YES
6.79/2.43	
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(14)
6.79/2.43	Obligation:
6.79/2.43	Rules:
6.79/2.43	f5(x18:0, x19:0) -> f5(x18:0 - 1, x19:0 - 1) :|: x19:0 > 0
6.79/2.43	
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(15) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
6.79/2.43	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
6.79/2.43	
6.79/2.43	   f5(x1, x2) -> f5(x2)
6.79/2.43	
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(16)
6.79/2.43	Obligation:
6.79/2.43	Rules:
6.79/2.43	f5(x19:0) -> f5(x19:0 - 1) :|: x19:0 > 0
6.79/2.43	
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(17) RankingReductionPairProof (EQUIVALENT)
6.79/2.43	Interpretation:
6.79/2.43	[ f5 ] = f5_1
6.79/2.43	
6.79/2.43	The following rules are decreasing:
6.79/2.43	f5(x19:0) -> f5(x19:0 - 1) :|: x19:0 > 0
6.79/2.43	
6.79/2.43	The following rules are bounded:
6.79/2.43	f5(x19:0) -> f5(x19:0 - 1) :|: x19:0 > 0
6.79/2.43	
6.79/2.43	
6.79/2.43	----------------------------------------
6.79/2.43	
6.79/2.43	(18)
6.79/2.43	YES
6.94/2.48	EOF