6.01/2.26	YES
6.01/2.27	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
6.01/2.27	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.01/2.27	
6.01/2.27	
6.01/2.27	Termination of the given C Problem could be proven:
6.01/2.27	
6.01/2.27	(0) C Problem
6.01/2.27	(1) CToIRSProof [EQUIVALENT, 0 ms]
6.01/2.27	(2) IntTRS
6.01/2.27	(3) TerminationGraphProcessor [SOUND, 46 ms]
6.01/2.27	(4) IntTRS
6.01/2.27	(5) IntTRSCompressionProof [EQUIVALENT, 25 ms]
6.01/2.27	(6) IntTRS
6.01/2.27	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
6.01/2.27	(8) IntTRS
6.01/2.27	(9) PolynomialOrderProcessor [EQUIVALENT, 1 ms]
6.01/2.27	(10) YES
6.01/2.27	
6.01/2.27	
6.01/2.27	----------------------------------------
6.01/2.27	
6.01/2.27	(0)
6.01/2.27	Obligation:
6.01/2.27	c file /export/starexec/sandbox/benchmark/theBenchmark.c
6.01/2.27	----------------------------------------
6.01/2.27	
6.01/2.27	(1) CToIRSProof (EQUIVALENT)
6.01/2.27	Parsed C Integer Program as IRS.
6.01/2.27	----------------------------------------
6.01/2.27	
6.01/2.27	(2)
6.01/2.27	Obligation:
6.01/2.27	Rules:
6.01/2.27	f1(i, j, k, t) -> f2(x_1, j, k, t) :|: TRUE
6.01/2.27	f2(x, x1, x2, x3) -> f3(x, x4, x2, x3) :|: TRUE
6.01/2.27	f3(x5, x6, x7, x8) -> f4(x5, x6, x9, x8) :|: TRUE
6.01/2.27	f5(x10, x11, x12, x13) -> f6(x11, x11, x12, x13) :|: TRUE
6.01/2.27	f6(x14, x15, x16, x17) -> f7(x14, arith, x16, x17) :|: TRUE && arith = x14 + 1
6.01/2.27	f7(x34, x35, x36, x37) -> f8(x34, x35, x38, x37) :|: TRUE && x38 = x36 - 1
6.01/2.27	f4(x22, x23, x24, x25) -> f5(x22, x23, x24, x25) :|: x22 <= 100 && x23 <= x24
6.01/2.27	f8(x26, x27, x28, x29) -> f4(x26, x27, x28, x29) :|: TRUE
6.01/2.27	f4(x30, x31, x32, x33) -> f9(x30, x31, x32, x33) :|: x30 > 100
6.01/2.27	f4(x39, x40, x41, x42) -> f9(x39, x40, x41, x42) :|: x40 > x41
6.01/2.27	Start term: f1(i, j, k, t)
6.01/2.27	
6.01/2.27	----------------------------------------
6.01/2.27	
6.01/2.27	(3) TerminationGraphProcessor (SOUND)
6.01/2.27	Constructed the termination graph and obtained one non-trivial SCC.
6.01/2.27	
6.01/2.27	----------------------------------------
6.01/2.27	
6.01/2.27	(4)
6.01/2.27	Obligation:
6.01/2.27	Rules:
6.01/2.27	f4(x22, x23, x24, x25) -> f5(x22, x23, x24, x25) :|: x22 <= 100 && x23 <= x24
6.01/2.27	f8(x26, x27, x28, x29) -> f4(x26, x27, x28, x29) :|: TRUE
6.01/2.27	f7(x34, x35, x36, x37) -> f8(x34, x35, x38, x37) :|: TRUE && x38 = x36 - 1
6.01/2.27	f6(x14, x15, x16, x17) -> f7(x14, arith, x16, x17) :|: TRUE && arith = x14 + 1
6.01/2.27	f5(x10, x11, x12, x13) -> f6(x11, x11, x12, x13) :|: TRUE
6.01/2.27	
6.01/2.27	----------------------------------------
6.01/2.27	
6.01/2.27	(5) IntTRSCompressionProof (EQUIVALENT)
6.01/2.27	Compressed rules.
6.01/2.27	----------------------------------------
6.01/2.27	
6.01/2.27	(6)
6.01/2.27	Obligation:
6.01/2.27	Rules:
6.01/2.27	f6(x14:0, x15:0, x16:0, x17:0) -> f6(x14:0 + 1, x14:0 + 1, x16:0 - 1, x17:0) :|: x14:0 < 101 && x16:0 - 1 >= x14:0 + 1
6.01/2.27	
6.01/2.27	----------------------------------------
6.01/2.27	
6.01/2.27	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
6.01/2.27	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
6.01/2.27	
6.01/2.27	   f6(x1, x2, x3, x4) -> f6(x1, x3)
6.01/2.27	
6.01/2.27	----------------------------------------
6.01/2.27	
6.01/2.27	(8)
6.01/2.27	Obligation:
6.01/2.27	Rules:
6.01/2.27	f6(x14:0, x16:0) -> f6(x14:0 + 1, x16:0 - 1) :|: x14:0 < 101 && x16:0 - 1 >= x14:0 + 1
6.01/2.27	
6.01/2.27	----------------------------------------
6.01/2.27	
6.01/2.27	(9) PolynomialOrderProcessor (EQUIVALENT)
6.01/2.27	Found the following polynomial interpretation:
6.01/2.27	[f6(x, x1)] = 100 - x
6.01/2.27	
6.01/2.27	The following rules are decreasing:
6.01/2.27	f6(x14:0, x16:0) -> f6(x14:0 + 1, x16:0 - 1) :|: x14:0 < 101 && x16:0 - 1 >= x14:0 + 1
6.01/2.27	The following rules are bounded:
6.01/2.27	f6(x14:0, x16:0) -> f6(x14:0 + 1, x16:0 - 1) :|: x14:0 < 101 && x16:0 - 1 >= x14:0 + 1
6.01/2.27	
6.01/2.27	----------------------------------------
6.01/2.27	
6.01/2.27	(10)
6.01/2.27	YES
6.23/2.30	EOF