4.52/1.97	YES
4.52/1.98	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.52/1.98	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.52/1.98	
4.52/1.98	
4.52/1.98	Termination of the given C Problem could be proven:
4.52/1.98	
4.52/1.98	(0) C Problem
4.52/1.98	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.52/1.98	(2) IntTRS
4.52/1.98	(3) TerminationGraphProcessor [SOUND, 46 ms]
4.52/1.98	(4) IntTRS
4.52/1.98	(5) IntTRSCompressionProof [EQUIVALENT, 28 ms]
4.52/1.98	(6) IntTRS
4.52/1.98	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.52/1.98	(8) IntTRS
4.52/1.98	(9) PolynomialOrderProcessor [EQUIVALENT, 15 ms]
4.52/1.98	(10) YES
4.52/1.98	
4.52/1.98	
4.52/1.98	----------------------------------------
4.52/1.98	
4.52/1.98	(0)
4.52/1.98	Obligation:
4.52/1.98	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.52/1.98	----------------------------------------
4.52/1.98	
4.52/1.98	(1) CToIRSProof (EQUIVALENT)
4.52/1.98	Parsed C Integer Program as IRS.
4.52/1.98	----------------------------------------
4.52/1.98	
4.52/1.98	(2)
4.52/1.98	Obligation:
4.52/1.98	Rules:
4.52/1.98	f1(x, y) -> f2(x_1, y) :|: TRUE
4.52/1.98	f2(x1, x2) -> f3(x1, x3) :|: TRUE
4.52/1.98	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 - x5
4.52/1.98	f5(x6, x7) -> f6(x6, x8) :|: TRUE
4.52/1.98	f3(x9, x10) -> f4(x9, x10) :|: x9 > x10 && x10 >= 1 && x10 <= 2
4.52/1.98	f6(x11, x12) -> f3(x11, x12) :|: TRUE
4.52/1.98	f3(x13, x14) -> f7(x13, x14) :|: x14 > 2
4.52/1.98	f3(x15, x16) -> f7(x15, x16) :|: x15 <= x16
4.52/1.98	f3(x17, x18) -> f7(x17, x18) :|: x18 < 1
4.52/1.98	Start term: f1(x, y)
4.52/1.98	
4.52/1.98	----------------------------------------
4.52/1.98	
4.52/1.98	(3) TerminationGraphProcessor (SOUND)
4.52/1.98	Constructed the termination graph and obtained one non-trivial SCC.
4.52/1.98	
4.52/1.98	----------------------------------------
4.52/1.98	
4.52/1.98	(4)
4.52/1.98	Obligation:
4.52/1.98	Rules:
4.52/1.98	f3(x9, x10) -> f4(x9, x10) :|: x9 > x10 && x10 >= 1 && x10 <= 2
4.52/1.98	f6(x11, x12) -> f3(x11, x12) :|: TRUE
4.52/1.98	f5(x6, x7) -> f6(x6, x8) :|: TRUE
4.52/1.98	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 - x5
4.52/1.98	
4.52/1.98	----------------------------------------
4.52/1.98	
4.52/1.98	(5) IntTRSCompressionProof (EQUIVALENT)
4.52/1.98	Compressed rules.
4.52/1.98	----------------------------------------
4.52/1.98	
4.52/1.98	(6)
4.52/1.98	Obligation:
4.52/1.98	Rules:
4.52/1.98	f5(x6:0, x7:0) -> f5(x6:0 - x8:0, x8:0) :|: x8:0 < x6:0 && x8:0 > 0 && x8:0 < 3
4.52/1.98	
4.52/1.98	----------------------------------------
4.52/1.98	
4.52/1.98	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.52/1.98	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.52/1.98	
4.52/1.98	   f5(x1, x2) -> f5(x1)
4.52/1.98	
4.52/1.98	----------------------------------------
4.52/1.98	
4.52/1.98	(8)
4.52/1.98	Obligation:
4.52/1.98	Rules:
4.52/1.98	f5(x6:0) -> f5(x6:0 - x8:0) :|: x8:0 < x6:0 && x8:0 > 0 && x8:0 < 3
4.52/1.98	
4.52/1.98	----------------------------------------
4.52/1.98	
4.52/1.98	(9) PolynomialOrderProcessor (EQUIVALENT)
4.52/1.98	Found the following polynomial interpretation:
4.52/1.98	[f5(x)] = x
4.52/1.98	
4.52/1.98	The following rules are decreasing:
4.52/1.98	f5(x6:0) -> f5(x6:0 - x8:0) :|: x8:0 < x6:0 && x8:0 > 0 && x8:0 < 3
4.52/1.98	The following rules are bounded:
4.52/1.98	f5(x6:0) -> f5(x6:0 - x8:0) :|: x8:0 < x6:0 && x8:0 > 0 && x8:0 < 3
4.52/1.98	
4.52/1.98	----------------------------------------
4.52/1.98	
4.52/1.98	(10)
4.52/1.98	YES
4.52/1.99	EOF