4.53/1.93	YES
4.65/1.95	proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
4.65/1.95	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.65/1.95	
4.65/1.95	
4.65/1.95	Termination of the given C Problem could be proven:
4.65/1.95	
4.65/1.95	(0) C Problem
4.65/1.95	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.65/1.95	(2) IntTRS
4.65/1.95	(3) TerminationGraphProcessor [SOUND, 51 ms]
4.65/1.95	(4) IntTRS
4.65/1.95	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
4.65/1.95	(6) IntTRS
4.65/1.95	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.65/1.95	(8) IntTRS
4.65/1.95	(9) RankingReductionPairProof [EQUIVALENT, 7 ms]
4.65/1.95	(10) YES
4.65/1.95	
4.65/1.95	
4.65/1.95	----------------------------------------
4.65/1.95	
4.65/1.95	(0)
4.65/1.95	Obligation:
4.65/1.95	c file /export/starexec/sandbox2/benchmark/theBenchmark.c
4.65/1.95	----------------------------------------
4.65/1.95	
4.65/1.95	(1) CToIRSProof (EQUIVALENT)
4.65/1.95	Parsed C Integer Program as IRS.
4.65/1.95	----------------------------------------
4.65/1.95	
4.65/1.95	(2)
4.65/1.95	Obligation:
4.65/1.95	Rules:
4.65/1.95	f1(c, x, y) -> f2(c, x_1, y) :|: TRUE
4.65/1.95	f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE
4.65/1.95	f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE
4.65/1.95	f5(x8, x9, x10) -> f6(x8, x9, arith) :|: TRUE && arith = x10 + 1
4.65/1.95	f6(x23, x24, x25) -> f7(x26, x24, x25) :|: TRUE && x26 = x23 + 1
4.65/1.95	f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x15 >= x16 + 1
4.65/1.95	f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE
4.65/1.95	f4(x20, x21, x22) -> f8(x20, x21, x22) :|: x21 < x22 + 1
4.65/1.95	Start term: f1(c, x, y)
4.65/1.95	
4.65/1.95	----------------------------------------
4.65/1.95	
4.65/1.95	(3) TerminationGraphProcessor (SOUND)
4.65/1.95	Constructed the termination graph and obtained one non-trivial SCC.
4.65/1.95	
4.65/1.95	----------------------------------------
4.65/1.95	
4.65/1.95	(4)
4.65/1.95	Obligation:
4.65/1.95	Rules:
4.65/1.95	f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x15 >= x16 + 1
4.65/1.95	f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE
4.65/1.95	f6(x23, x24, x25) -> f7(x26, x24, x25) :|: TRUE && x26 = x23 + 1
4.65/1.95	f5(x8, x9, x10) -> f6(x8, x9, arith) :|: TRUE && arith = x10 + 1
4.65/1.95	
4.65/1.95	----------------------------------------
4.65/1.95	
4.65/1.95	(5) IntTRSCompressionProof (EQUIVALENT)
4.65/1.95	Compressed rules.
4.65/1.95	----------------------------------------
4.65/1.95	
4.65/1.95	(6)
4.65/1.95	Obligation:
4.65/1.95	Rules:
4.65/1.95	f6(x23:0, x24:0, x25:0) -> f6(x23:0 + 1, x24:0, x25:0 + 1) :|: x25:0 + 1 <= x24:0
4.65/1.95	
4.65/1.95	----------------------------------------
4.65/1.95	
4.65/1.95	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.65/1.95	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.65/1.95	
4.65/1.95	   f6(x1, x2, x3) -> f6(x2, x3)
4.65/1.95	
4.65/1.95	----------------------------------------
4.65/1.95	
4.65/1.95	(8)
4.65/1.95	Obligation:
4.65/1.95	Rules:
4.65/1.95	f6(x24:0, x25:0) -> f6(x24:0, x25:0 + 1) :|: x25:0 + 1 <= x24:0
4.65/1.95	
4.65/1.95	----------------------------------------
4.65/1.95	
4.65/1.95	(9) RankingReductionPairProof (EQUIVALENT)
4.65/1.95	Interpretation:
4.65/1.95	[ f6 ] = -1*f6_2 + f6_1
4.65/1.95	
4.65/1.95	The following rules are decreasing:
4.65/1.95	f6(x24:0, x25:0) -> f6(x24:0, x25:0 + 1) :|: x25:0 + 1 <= x24:0
4.65/1.95	
4.65/1.95	The following rules are bounded:
4.65/1.95	f6(x24:0, x25:0) -> f6(x24:0, x25:0 + 1) :|: x25:0 + 1 <= x24:0
4.65/1.95	
4.65/1.95	
4.65/1.95	----------------------------------------
4.65/1.95	
4.65/1.95	(10)
4.65/1.95	YES
4.65/1.99	EOF