4.58/1.96	YES
4.58/1.96	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.58/1.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.58/1.96	
4.58/1.96	
4.58/1.96	Termination of the given C Problem could be proven:
4.58/1.96	
4.58/1.96	(0) C Problem
4.58/1.96	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.58/1.96	(2) IntTRS
4.58/1.96	(3) TerminationGraphProcessor [SOUND, 52 ms]
4.58/1.96	(4) IntTRS
4.58/1.96	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
4.58/1.96	(6) IntTRS
4.58/1.96	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.58/1.96	(8) IntTRS
4.58/1.96	(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
4.58/1.96	(10) YES
4.58/1.96	
4.58/1.96	
4.58/1.96	----------------------------------------
4.58/1.96	
4.58/1.96	(0)
4.58/1.96	Obligation:
4.58/1.96	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.58/1.96	----------------------------------------
4.58/1.96	
4.58/1.96	(1) CToIRSProof (EQUIVALENT)
4.58/1.96	Parsed C Integer Program as IRS.
4.58/1.96	----------------------------------------
4.58/1.96	
4.58/1.96	(2)
4.58/1.96	Obligation:
4.58/1.96	Rules:
4.58/1.96	f1(x, y, oldx) -> f2(x_1, y, oldx) :|: TRUE
4.58/1.96	f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
4.58/1.96	f4(x5, x6, x7) -> f5(x5, x6, x5) :|: TRUE
4.58/1.96	f5(x8, x9, x10) -> f6(arith, x9, x10) :|: TRUE && arith = x9 - 1
4.58/1.96	f6(x23, x24, x25) -> f7(x23, x26, x25) :|: TRUE && x26 = x25 - 1
4.58/1.97	f3(x14, x15, x16) -> f4(x14, x15, x16) :|: x14 >= 0 && x15 >= 0
4.58/1.97	f7(x17, x18, x19) -> f3(x17, x18, x19) :|: TRUE
4.58/1.97	f3(x20, x21, x22) -> f8(x20, x21, x22) :|: x20 < 0
4.58/1.97	f3(x27, x28, x29) -> f8(x27, x28, x29) :|: x28 < 0
4.58/1.97	Start term: f1(x, y, oldx)
4.58/1.97	
4.58/1.97	----------------------------------------
4.58/1.97	
4.58/1.97	(3) TerminationGraphProcessor (SOUND)
4.58/1.97	Constructed the termination graph and obtained one non-trivial SCC.
4.58/1.97	
4.58/1.97	----------------------------------------
4.58/1.97	
4.58/1.97	(4)
4.58/1.97	Obligation:
4.58/1.97	Rules:
4.58/1.97	f3(x14, x15, x16) -> f4(x14, x15, x16) :|: x14 >= 0 && x15 >= 0
4.58/1.97	f7(x17, x18, x19) -> f3(x17, x18, x19) :|: TRUE
4.58/1.97	f6(x23, x24, x25) -> f7(x23, x26, x25) :|: TRUE && x26 = x25 - 1
4.58/1.97	f5(x8, x9, x10) -> f6(arith, x9, x10) :|: TRUE && arith = x9 - 1
4.58/1.97	f4(x5, x6, x7) -> f5(x5, x6, x5) :|: TRUE
4.58/1.97	
4.58/1.97	----------------------------------------
4.58/1.97	
4.58/1.97	(5) IntTRSCompressionProof (EQUIVALENT)
4.58/1.97	Compressed rules.
4.58/1.97	----------------------------------------
4.58/1.97	
4.58/1.97	(6)
4.58/1.97	Obligation:
4.58/1.97	Rules:
4.58/1.97	f5(x8:0, x9:0, x10:0) -> f5(x9:0 - 1, x10:0 - 1, x9:0 - 1) :|: x9:0 > 0 && x10:0 > 0
4.58/1.97	
4.58/1.97	----------------------------------------
4.58/1.97	
4.58/1.97	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.58/1.97	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.58/1.97	
4.58/1.97	   f5(x1, x2, x3) -> f5(x2, x3)
4.58/1.97	
4.58/1.97	----------------------------------------
4.58/1.97	
4.58/1.97	(8)
4.58/1.97	Obligation:
4.58/1.97	Rules:
4.58/1.97	f5(x9:0, x10:0) -> f5(x10:0 - 1, x9:0 - 1) :|: x9:0 > 0 && x10:0 > 0
4.58/1.97	
4.58/1.97	----------------------------------------
4.58/1.97	
4.58/1.97	(9) PolynomialOrderProcessor (EQUIVALENT)
4.58/1.97	Found the following polynomial interpretation:
4.58/1.97	[f5(x, x1)] = -1 + x + x1
4.58/1.97	
4.58/1.97	The following rules are decreasing:
4.58/1.97	f5(x9:0, x10:0) -> f5(x10:0 - 1, x9:0 - 1) :|: x9:0 > 0 && x10:0 > 0
4.58/1.97	The following rules are bounded:
4.58/1.97	f5(x9:0, x10:0) -> f5(x10:0 - 1, x9:0 - 1) :|: x9:0 > 0 && x10:0 > 0
4.58/1.97	
4.58/1.97	----------------------------------------
4.58/1.97	
4.58/1.97	(10)
4.58/1.97	YES
4.58/2.00	EOF