4.66/1.96	YES
4.66/1.97	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.66/1.97	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.66/1.97	
4.66/1.97	
4.66/1.97	Termination of the given C Problem could be proven:
4.66/1.97	
4.66/1.97	(0) C Problem
4.66/1.97	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.66/1.97	(2) IntTRS
4.66/1.97	(3) TerminationGraphProcessor [SOUND, 43 ms]
4.66/1.97	(4) IntTRS
4.66/1.97	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
4.66/1.97	(6) IntTRS
4.66/1.97	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.66/1.97	(8) IntTRS
4.66/1.97	(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
4.66/1.97	(10) YES
4.66/1.97	
4.66/1.97	
4.66/1.97	----------------------------------------
4.66/1.97	
4.66/1.97	(0)
4.66/1.97	Obligation:
4.66/1.97	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.66/1.97	----------------------------------------
4.66/1.97	
4.66/1.97	(1) CToIRSProof (EQUIVALENT)
4.66/1.97	Parsed C Integer Program as IRS.
4.66/1.97	----------------------------------------
4.66/1.97	
4.66/1.97	(2)
4.66/1.97	Obligation:
4.66/1.97	Rules:
4.66/1.97	f1(x, oldx) -> f2(x_1, oldx) :|: TRUE
4.66/1.97	f3(x1, x2) -> f4(x1, x1) :|: TRUE
4.66/1.97	f4(x3, x4) -> f5(x5, x4) :|: TRUE
4.66/1.97	f2(x6, x7) -> f3(x6, x7) :|: x6 > 0 && 2 * x6 <= x7
4.66/1.97	f5(x8, x9) -> f2(x8, x9) :|: TRUE
4.66/1.97	f2(x10, x11) -> f6(x10, x11) :|: x10 <= 0
4.66/1.97	f2(x12, x13) -> f6(x12, x13) :|: 2 * x12 > x13
4.66/1.97	Start term: f1(x, oldx)
4.66/1.97	
4.66/1.97	----------------------------------------
4.66/1.97	
4.66/1.97	(3) TerminationGraphProcessor (SOUND)
4.66/1.97	Constructed the termination graph and obtained one non-trivial SCC.
4.66/1.97	
4.66/1.97	----------------------------------------
4.66/1.97	
4.66/1.97	(4)
4.66/1.97	Obligation:
4.66/1.97	Rules:
4.66/1.97	f2(x6, x7) -> f3(x6, x7) :|: x6 > 0 && 2 * x6 <= x7
4.66/1.97	f5(x8, x9) -> f2(x8, x9) :|: TRUE
4.66/1.97	f4(x3, x4) -> f5(x5, x4) :|: TRUE
4.66/1.97	f3(x1, x2) -> f4(x1, x1) :|: TRUE
4.66/1.97	
4.66/1.97	----------------------------------------
4.66/1.97	
4.66/1.97	(5) IntTRSCompressionProof (EQUIVALENT)
4.66/1.97	Compressed rules.
4.66/1.97	----------------------------------------
4.66/1.97	
4.66/1.97	(6)
4.66/1.97	Obligation:
4.66/1.97	Rules:
4.66/1.97	f4(x3:0, x4:0) -> f4(x5:0, x5:0) :|: x5:0 > 0 && x4:0 >= 2 * x5:0
4.66/1.97	
4.66/1.97	----------------------------------------
4.66/1.97	
4.66/1.97	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.66/1.97	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.66/1.97	
4.66/1.97	   f4(x1, x2) -> f4(x2)
4.66/1.97	
4.66/1.97	----------------------------------------
4.66/1.97	
4.66/1.97	(8)
4.66/1.97	Obligation:
4.66/1.97	Rules:
4.66/1.97	f4(x4:0) -> f4(x5:0) :|: x5:0 > 0 && x4:0 >= 2 * x5:0
4.66/1.97	
4.66/1.97	----------------------------------------
4.66/1.97	
4.66/1.97	(9) PolynomialOrderProcessor (EQUIVALENT)
4.66/1.97	Found the following polynomial interpretation:
4.66/1.97	[f4(x)] = x
4.66/1.97	
4.66/1.97	The following rules are decreasing:
4.66/1.97	f4(x4:0) -> f4(x5:0) :|: x5:0 > 0 && x4:0 >= 2 * x5:0
4.66/1.97	The following rules are bounded:
4.66/1.97	f4(x4:0) -> f4(x5:0) :|: x5:0 > 0 && x4:0 >= 2 * x5:0
4.66/1.97	
4.66/1.97	----------------------------------------
4.66/1.97	
4.66/1.97	(10)
4.66/1.97	YES
4.93/2.01	EOF