4.82/2.00	YES
4.82/2.02	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.82/2.02	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.82/2.02	
4.82/2.02	
4.82/2.02	Termination of the given C Problem could be proven:
4.82/2.02	
4.82/2.02	(0) C Problem
4.82/2.02	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.82/2.02	(2) IntTRS
4.82/2.02	(3) TerminationGraphProcessor [SOUND, 55 ms]
4.82/2.02	(4) IntTRS
4.82/2.02	(5) IntTRSCompressionProof [EQUIVALENT, 29 ms]
4.82/2.02	(6) IntTRS
4.82/2.02	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.82/2.02	(8) IntTRS
4.82/2.02	(9) PolynomialOrderProcessor [EQUIVALENT, 13 ms]
4.82/2.02	(10) YES
4.82/2.02	
4.82/2.02	
4.82/2.02	----------------------------------------
4.82/2.02	
4.82/2.02	(0)
4.82/2.02	Obligation:
4.82/2.02	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.82/2.02	----------------------------------------
4.82/2.02	
4.82/2.02	(1) CToIRSProof (EQUIVALENT)
4.82/2.02	Parsed C Integer Program as IRS.
4.82/2.02	----------------------------------------
4.82/2.02	
4.82/2.02	(2)
4.82/2.02	Obligation:
4.82/2.02	Rules:
4.82/2.02	f1(k, i, j, tmp) -> f2(x_1, i, j, tmp) :|: TRUE
4.82/2.02	f2(x, x1, x2, x3) -> f3(x, x4, x2, x3) :|: TRUE
4.82/2.02	f3(x5, x6, x7, x8) -> f4(x5, x6, x9, x8) :|: TRUE
4.82/2.02	f5(x10, x11, x12, x13) -> f6(x10, x11, x12, x11) :|: TRUE
4.82/2.02	f6(x14, x15, x16, x17) -> f7(x14, x16, x16, x17) :|: TRUE
4.82/2.02	f7(x18, x19, x20, x21) -> f8(x18, x19, arith, x21) :|: TRUE && arith = x21 + 1
4.82/2.02	f8(x38, x39, x40, x41) -> f9(x42, x39, x40, x41) :|: TRUE && x42 = x38 - 1
4.82/2.02	f4(x26, x27, x28, x29) -> f5(x26, x27, x28, x29) :|: x27 <= 100 && x28 <= x26
4.82/2.02	f9(x30, x31, x32, x33) -> f4(x30, x31, x32, x33) :|: TRUE
4.82/2.02	f4(x34, x35, x36, x37) -> f10(x34, x35, x36, x37) :|: x35 > 100
4.82/2.02	f4(x43, x44, x45, x46) -> f10(x43, x44, x45, x46) :|: x45 > x43
4.82/2.02	Start term: f1(k, i, j, tmp)
4.82/2.02	
4.82/2.02	----------------------------------------
4.82/2.02	
4.82/2.02	(3) TerminationGraphProcessor (SOUND)
4.82/2.02	Constructed the termination graph and obtained one non-trivial SCC.
4.82/2.02	
4.82/2.02	----------------------------------------
4.82/2.02	
4.82/2.02	(4)
4.82/2.02	Obligation:
4.82/2.02	Rules:
4.82/2.02	f4(x26, x27, x28, x29) -> f5(x26, x27, x28, x29) :|: x27 <= 100 && x28 <= x26
4.82/2.02	f9(x30, x31, x32, x33) -> f4(x30, x31, x32, x33) :|: TRUE
4.82/2.02	f8(x38, x39, x40, x41) -> f9(x42, x39, x40, x41) :|: TRUE && x42 = x38 - 1
4.82/2.02	f7(x18, x19, x20, x21) -> f8(x18, x19, arith, x21) :|: TRUE && arith = x21 + 1
4.82/2.02	f6(x14, x15, x16, x17) -> f7(x14, x16, x16, x17) :|: TRUE
4.82/2.02	f5(x10, x11, x12, x13) -> f6(x10, x11, x12, x11) :|: TRUE
4.82/2.02	
4.82/2.02	----------------------------------------
4.82/2.02	
4.82/2.02	(5) IntTRSCompressionProof (EQUIVALENT)
4.82/2.02	Compressed rules.
4.82/2.02	----------------------------------------
4.82/2.02	
4.82/2.02	(6)
4.82/2.02	Obligation:
4.82/2.02	Rules:
4.82/2.02	f6(x14:0, x15:0, x16:0, x17:0) -> f6(x14:0 - 1, x16:0, x17:0 + 1, x16:0) :|: x16:0 < 101 && x17:0 + 1 <= x14:0 - 1
4.82/2.02	
4.82/2.02	----------------------------------------
4.82/2.02	
4.82/2.02	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.82/2.02	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.82/2.02	
4.82/2.02	   f6(x1, x2, x3, x4) -> f6(x1, x3, x4)
4.82/2.02	
4.82/2.02	----------------------------------------
4.82/2.02	
4.82/2.02	(8)
4.82/2.02	Obligation:
4.82/2.02	Rules:
4.82/2.02	f6(x14:0, x16:0, x17:0) -> f6(x14:0 - 1, x17:0 + 1, x16:0) :|: x16:0 < 101 && x17:0 + 1 <= x14:0 - 1
4.82/2.02	
4.82/2.02	----------------------------------------
4.82/2.02	
4.82/2.02	(9) PolynomialOrderProcessor (EQUIVALENT)
4.82/2.02	Found the following polynomial interpretation:
4.82/2.02	[f6(x, x1, x2)] = 98 + x - x1 - x2
4.82/2.02	
4.82/2.02	The following rules are decreasing:
4.82/2.02	f6(x14:0, x16:0, x17:0) -> f6(x14:0 - 1, x17:0 + 1, x16:0) :|: x16:0 < 101 && x17:0 + 1 <= x14:0 - 1
4.82/2.02	The following rules are bounded:
4.82/2.02	f6(x14:0, x16:0, x17:0) -> f6(x14:0 - 1, x17:0 + 1, x16:0) :|: x16:0 < 101 && x17:0 + 1 <= x14:0 - 1
4.82/2.02	
4.82/2.02	----------------------------------------
4.82/2.02	
4.82/2.02	(10)
4.82/2.02	YES
5.04/2.05	EOF