4.20/1.79	YES
4.20/1.81	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.20/1.81	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.20/1.81	
4.20/1.81	
4.20/1.81	Termination of the given C Problem could be proven:
4.20/1.81	
4.20/1.81	(0) C Problem
4.20/1.81	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.20/1.81	(2) IntTRS
4.20/1.81	(3) TerminationGraphProcessor [SOUND, 51 ms]
4.20/1.81	(4) IntTRS
4.20/1.81	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
4.20/1.81	(6) IntTRS
4.20/1.81	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.20/1.81	(8) IntTRS
4.20/1.81	(9) PolynomialOrderProcessor [EQUIVALENT, 6 ms]
4.20/1.81	(10) YES
4.20/1.81	
4.20/1.81	
4.20/1.81	----------------------------------------
4.20/1.81	
4.20/1.81	(0)
4.20/1.81	Obligation:
4.20/1.81	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.20/1.81	----------------------------------------
4.20/1.81	
4.20/1.81	(1) CToIRSProof (EQUIVALENT)
4.20/1.81	Parsed C Integer Program as IRS.
4.20/1.81	----------------------------------------
4.20/1.81	
4.20/1.81	(2)
4.20/1.81	Obligation:
4.20/1.81	Rules:
4.20/1.81	f1(x, y, z) -> f2(12, y, z) :|: TRUE
4.20/1.81	f2(x1, x2, x3) -> f3(x1, 0, x3) :|: TRUE
4.20/1.81	f3(x4, x5, x6) -> f4(x4, x5, x7) :|: TRUE
4.20/1.81	f5(x8, x9, x10) -> f6(arith, x9, x10) :|: TRUE && arith = x8 + 1
4.20/1.81	f6(x26, x27, x28) -> f7(x26, x29, x28) :|: TRUE && x29 = x27 - 1
4.20/1.81	f7(x30, x31, x32) -> f8(x30, x31, x33) :|: TRUE && x33 = x32 - 1
4.20/1.81	f4(x17, x18, x19) -> f5(x17, x18, x19) :|: x19 > 0
4.20/1.81	f8(x20, x21, x22) -> f4(x20, x21, x22) :|: TRUE
4.20/1.81	f4(x23, x24, x25) -> f9(x23, x24, x25) :|: x25 <= 0
4.20/1.81	Start term: f1(x, y, z)
4.20/1.81	
4.20/1.81	----------------------------------------
4.20/1.81	
4.20/1.81	(3) TerminationGraphProcessor (SOUND)
4.20/1.81	Constructed the termination graph and obtained one non-trivial SCC.
4.20/1.81	
4.20/1.81	----------------------------------------
4.20/1.81	
4.20/1.81	(4)
4.20/1.81	Obligation:
4.20/1.81	Rules:
4.20/1.81	f4(x17, x18, x19) -> f5(x17, x18, x19) :|: x19 > 0
4.20/1.81	f8(x20, x21, x22) -> f4(x20, x21, x22) :|: TRUE
4.20/1.81	f7(x30, x31, x32) -> f8(x30, x31, x33) :|: TRUE && x33 = x32 - 1
4.20/1.81	f6(x26, x27, x28) -> f7(x26, x29, x28) :|: TRUE && x29 = x27 - 1
4.20/1.81	f5(x8, x9, x10) -> f6(arith, x9, x10) :|: TRUE && arith = x8 + 1
4.20/1.81	
4.20/1.81	----------------------------------------
4.20/1.81	
4.20/1.81	(5) IntTRSCompressionProof (EQUIVALENT)
4.20/1.81	Compressed rules.
4.20/1.81	----------------------------------------
4.20/1.81	
4.20/1.81	(6)
4.20/1.81	Obligation:
4.20/1.81	Rules:
4.20/1.81	f6(x26:0, x27:0, x28:0) -> f6(x26:0 + 1, x27:0 - 1, x28:0 - 1) :|: x28:0 > 1
4.20/1.81	
4.20/1.81	----------------------------------------
4.20/1.81	
4.20/1.81	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.20/1.81	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.20/1.81	
4.20/1.81	   f6(x1, x2, x3) -> f6(x3)
4.20/1.81	
4.20/1.81	----------------------------------------
4.20/1.81	
4.20/1.81	(8)
4.20/1.81	Obligation:
4.20/1.81	Rules:
4.20/1.81	f6(x28:0) -> f6(x28:0 - 1) :|: x28:0 > 1
4.20/1.81	
4.20/1.81	----------------------------------------
4.20/1.81	
4.20/1.81	(9) PolynomialOrderProcessor (EQUIVALENT)
4.20/1.81	Found the following polynomial interpretation:
4.20/1.81	[f6(x)] = x
4.20/1.81	
4.20/1.81	The following rules are decreasing:
4.20/1.81	f6(x28:0) -> f6(x28:0 - 1) :|: x28:0 > 1
4.20/1.81	The following rules are bounded:
4.20/1.81	f6(x28:0) -> f6(x28:0 - 1) :|: x28:0 > 1
4.20/1.81	
4.20/1.81	----------------------------------------
4.20/1.81	
4.20/1.81	(10)
4.20/1.81	YES
4.44/1.84	EOF