5.00/2.27	YES
5.65/2.29	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
5.65/2.29	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.65/2.29	
5.65/2.29	
5.65/2.29	Termination of the given C Problem could be proven:
5.65/2.29	
5.65/2.29	(0) C Problem
5.65/2.29	(1) CToIRSProof [EQUIVALENT, 0 ms]
5.65/2.29	(2) IntTRS
5.65/2.29	(3) TerminationGraphProcessor [SOUND, 53 ms]
5.65/2.29	(4) IntTRS
5.65/2.29	(5) IntTRSCompressionProof [EQUIVALENT, 40 ms]
5.65/2.29	(6) IntTRS
5.65/2.29	(7) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
5.65/2.29	(8) IntTRS
5.65/2.29	(9) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
5.65/2.29	(10) IntTRS
5.65/2.29	(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
5.65/2.29	(12) YES
5.65/2.29	
5.65/2.29	
5.65/2.29	----------------------------------------
5.65/2.29	
5.65/2.29	(0)
5.65/2.29	Obligation:
5.65/2.29	c file /export/starexec/sandbox/benchmark/theBenchmark.c
5.65/2.29	----------------------------------------
5.65/2.29	
5.65/2.29	(1) CToIRSProof (EQUIVALENT)
5.65/2.29	Parsed C Integer Program as IRS.
5.65/2.29	----------------------------------------
5.65/2.29	
5.65/2.29	(2)
5.65/2.29	Obligation:
5.65/2.29	Rules:
5.65/2.29	f1(x, y) -> f2(x_1, y) :|: TRUE
5.65/2.29	f2(x1, x2) -> f3(x1, x3) :|: TRUE
5.65/2.29	f5(x4, x5) -> f6(x4, arith) :|: TRUE && arith = x5 - 1
5.65/2.29	f4(x6, x7) -> f5(x6, x7) :|: x7 > 0
5.65/2.29	f6(x8, x9) -> f4(x8, x9) :|: TRUE
5.65/2.29	f4(x10, x11) -> f7(x10, x11) :|: x11 <= 0
5.65/2.29	f7(x20, x21) -> f8(x22, x21) :|: TRUE && x22 = x20 - 1
5.65/2.29	f3(x14, x15) -> f4(x14, x15) :|: x14 > 0
5.65/2.29	f8(x16, x17) -> f3(x16, x17) :|: TRUE
5.65/2.29	f3(x18, x19) -> f9(x18, x19) :|: x18 <= 0
5.65/2.29	Start term: f1(x, y)
5.65/2.29	
5.65/2.29	----------------------------------------
5.65/2.29	
5.65/2.29	(3) TerminationGraphProcessor (SOUND)
5.65/2.29	Constructed the termination graph and obtained one non-trivial SCC.
5.65/2.29	
5.65/2.29	----------------------------------------
5.65/2.29	
5.65/2.29	(4)
5.65/2.29	Obligation:
5.65/2.29	Rules:
5.65/2.29	f3(x14, x15) -> f4(x14, x15) :|: x14 > 0
5.65/2.29	f8(x16, x17) -> f3(x16, x17) :|: TRUE
5.65/2.29	f7(x20, x21) -> f8(x22, x21) :|: TRUE && x22 = x20 - 1
5.65/2.29	f4(x10, x11) -> f7(x10, x11) :|: x11 <= 0
5.65/2.29	f6(x8, x9) -> f4(x8, x9) :|: TRUE
5.65/2.29	f5(x4, x5) -> f6(x4, arith) :|: TRUE && arith = x5 - 1
5.65/2.29	f4(x6, x7) -> f5(x6, x7) :|: x7 > 0
5.65/2.29	
5.65/2.29	----------------------------------------
5.65/2.29	
5.65/2.29	(5) IntTRSCompressionProof (EQUIVALENT)
5.65/2.29	Compressed rules.
5.65/2.29	----------------------------------------
5.65/2.29	
5.65/2.29	(6)
5.65/2.29	Obligation:
5.65/2.29	Rules:
5.65/2.29	f4(x6:0, x7:0) -> f4(x6:0, x7:0 - 1) :|: x7:0 > 0
5.65/2.29	f4(x10:0, x11:0) -> f4(x10:0 - 1, x11:0) :|: x11:0 < 1 && x10:0 > 1
5.65/2.29	
5.65/2.29	----------------------------------------
5.65/2.29	
5.65/2.29	(7) PolynomialOrderProcessor (EQUIVALENT)
5.65/2.29	Found the following polynomial interpretation:
5.65/2.29	[f4(x, x1)] = -1 + x
5.65/2.29	
5.65/2.29	The following rules are decreasing:
5.65/2.29	f4(x10:0, x11:0) -> f4(x10:0 - 1, x11:0) :|: x11:0 < 1 && x10:0 > 1
5.65/2.29	The following rules are bounded:
5.65/2.29	f4(x10:0, x11:0) -> f4(x10:0 - 1, x11:0) :|: x11:0 < 1 && x10:0 > 1
5.65/2.29	
5.65/2.29	----------------------------------------
5.65/2.29	
5.65/2.29	(8)
5.65/2.29	Obligation:
5.65/2.29	Rules:
5.65/2.29	f4(x6:0, x7:0) -> f4(x6:0, x7:0 - 1) :|: x7:0 > 0
5.65/2.29	
5.65/2.29	----------------------------------------
5.65/2.29	
5.65/2.29	(9) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
5.65/2.29	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
5.65/2.29	
5.65/2.29	   f4(x1, x2) -> f4(x2)
5.65/2.29	
5.65/2.29	----------------------------------------
5.65/2.29	
5.65/2.29	(10)
5.65/2.29	Obligation:
5.65/2.29	Rules:
5.65/2.29	f4(x7:0) -> f4(x7:0 - 1) :|: x7:0 > 0
5.65/2.29	
5.65/2.29	----------------------------------------
5.65/2.29	
5.65/2.29	(11) PolynomialOrderProcessor (EQUIVALENT)
5.65/2.29	Found the following polynomial interpretation:
5.65/2.29	[f4(x)] = x
5.65/2.29	
5.65/2.29	The following rules are decreasing:
5.65/2.29	f4(x7:0) -> f4(x7:0 - 1) :|: x7:0 > 0
5.65/2.29	The following rules are bounded:
5.65/2.29	f4(x7:0) -> f4(x7:0 - 1) :|: x7:0 > 0
5.65/2.29	
5.65/2.29	----------------------------------------
5.65/2.29	
5.65/2.29	(12)
5.65/2.29	YES
5.67/2.32	EOF