4.02/1.84	YES
4.31/1.94	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.31/1.94	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.31/1.94	
4.31/1.94	
4.31/1.94	Termination of the given C Problem could be proven:
4.31/1.94	
4.31/1.94	(0) C Problem
4.31/1.94	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.31/1.94	(2) IntTRS
4.31/1.94	(3) TerminationGraphProcessor [SOUND, 16 ms]
4.31/1.94	(4) IntTRS
4.31/1.94	(5) IntTRSCompressionProof [EQUIVALENT, 12 ms]
4.31/1.94	(6) IntTRS
4.31/1.94	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.31/1.94	(8) IntTRS
4.31/1.94	(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
4.31/1.94	(10) YES
4.31/1.94	
4.31/1.94	
4.31/1.94	----------------------------------------
4.31/1.94	
4.31/1.94	(0)
4.31/1.94	Obligation:
4.31/1.94	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.31/1.94	----------------------------------------
4.31/1.94	
4.31/1.94	(1) CToIRSProof (EQUIVALENT)
4.31/1.94	Parsed C Integer Program as IRS.
4.31/1.94	----------------------------------------
4.31/1.94	
4.31/1.94	(2)
4.31/1.94	Obligation:
4.31/1.94	Rules:
4.31/1.94	f1(i, c) -> f2(0, c) :|: TRUE
4.31/1.94	f2(x, x1) -> f3(x, 0) :|: TRUE
4.31/1.94	f4(x2, x3) -> f5(arith, x3) :|: TRUE && arith = x2 + 1
4.31/1.94	f5(x12, x13) -> f6(x12, x14) :|: TRUE && x14 = x13 + 1
4.31/1.94	f3(x6, x7) -> f4(x6, x7) :|: x6 <= 10
4.31/1.94	f6(x8, x9) -> f3(x8, x9) :|: TRUE
4.31/1.94	f3(x10, x11) -> f7(x10, x11) :|: x10 > 10
4.31/1.94	Start term: f1(i, c)
4.31/1.94	
4.31/1.94	----------------------------------------
4.31/1.94	
4.31/1.94	(3) TerminationGraphProcessor (SOUND)
4.31/1.94	Constructed the termination graph and obtained one non-trivial SCC.
4.31/1.94	
4.31/1.94	----------------------------------------
4.31/1.94	
4.31/1.94	(4)
4.31/1.94	Obligation:
4.31/1.94	Rules:
4.31/1.94	f3(x6, x7) -> f4(x6, x7) :|: x6 <= 10
4.31/1.94	f6(x8, x9) -> f3(x8, x9) :|: TRUE
4.31/1.94	f5(x12, x13) -> f6(x12, x14) :|: TRUE && x14 = x13 + 1
4.31/1.94	f4(x2, x3) -> f5(arith, x3) :|: TRUE && arith = x2 + 1
4.31/1.94	
4.31/1.94	----------------------------------------
4.31/1.94	
4.31/1.94	(5) IntTRSCompressionProof (EQUIVALENT)
4.31/1.94	Compressed rules.
4.31/1.94	----------------------------------------
4.31/1.94	
4.31/1.94	(6)
4.31/1.94	Obligation:
4.31/1.94	Rules:
4.31/1.94	f5(x12:0, x13:0) -> f5(x12:0 + 1, x13:0 + 1) :|: x12:0 < 11
4.31/1.94	
4.31/1.94	----------------------------------------
4.31/1.94	
4.31/1.94	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.31/1.94	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.31/1.94	
4.31/1.94	   f5(x1, x2) -> f5(x1)
4.31/1.94	
4.31/1.94	----------------------------------------
4.31/1.94	
4.31/1.94	(8)
4.31/1.94	Obligation:
4.31/1.94	Rules:
4.31/1.94	f5(x12:0) -> f5(x12:0 + 1) :|: x12:0 < 11
4.31/1.94	
4.31/1.94	----------------------------------------
4.31/1.94	
4.31/1.94	(9) PolynomialOrderProcessor (EQUIVALENT)
4.31/1.94	Found the following polynomial interpretation:
4.31/1.94	[f5(x)] = 10 - x
4.31/1.94	
4.31/1.94	The following rules are decreasing:
4.31/1.94	f5(x12:0) -> f5(x12:0 + 1) :|: x12:0 < 11
4.31/1.94	The following rules are bounded:
4.31/1.94	f5(x12:0) -> f5(x12:0 + 1) :|: x12:0 < 11
4.31/1.94	
4.31/1.94	----------------------------------------
4.31/1.94	
4.31/1.94	(10)
4.31/1.94	YES
4.31/1.96	EOF