4.79/2.50	YES
4.79/2.51	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.79/2.51	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.79/2.51	
4.79/2.51	
4.79/2.51	Termination of the given C Problem could be proven:
4.79/2.51	
4.79/2.51	(0) C Problem
4.79/2.51	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.79/2.51	(2) IntTRS
4.79/2.51	(3) TerminationGraphProcessor [SOUND, 54 ms]
4.79/2.51	(4) IntTRS
4.79/2.51	(5) IntTRSCompressionProof [EQUIVALENT, 42 ms]
4.79/2.51	(6) IntTRS
4.79/2.51	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.79/2.51	(8) IntTRS
4.79/2.51	(9) PolynomialOrderProcessor [EQUIVALENT, 11 ms]
4.79/2.51	(10) YES
4.79/2.51	
4.79/2.51	
4.79/2.51	----------------------------------------
4.79/2.51	
4.79/2.51	(0)
4.79/2.51	Obligation:
4.79/2.51	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.79/2.51	----------------------------------------
4.79/2.51	
4.79/2.51	(1) CToIRSProof (EQUIVALENT)
4.79/2.51	Parsed C Integer Program as IRS.
4.79/2.51	----------------------------------------
4.79/2.51	
4.79/2.51	(2)
4.79/2.51	Obligation:
4.79/2.51	Rules:
4.79/2.51	f1(x, y, z) -> f2(x_1, y, z) :|: TRUE
4.79/2.51	f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
4.79/2.51	f3(x5, x6, x7) -> f4(x5, x6, x8) :|: TRUE
4.79/2.51	f5(x9, x10, x11) -> f6(arith, x10, x11) :|: TRUE && arith = 0 - x9 + x10
4.79/2.51	f6(x12, x13, x14) -> f7(x12, x14, x14) :|: TRUE
4.79/2.51	f7(x15, x16, x17) -> f8(x15, x16, x17) :|: TRUE
4.79/2.51	f8(x30, x31, x32) -> f9(x30, x31, x33) :|: TRUE && x33 = x32 + 1
4.79/2.51	f4(x21, x22, x23) -> f5(x21, x22, x23) :|: x21 - x22 > 0
4.79/2.51	f9(x24, x25, x26) -> f4(x24, x25, x26) :|: TRUE
4.79/2.51	f4(x27, x28, x29) -> f10(x27, x28, x29) :|: x27 - x28 <= 0
4.79/2.51	Start term: f1(x, y, z)
4.79/2.51	
4.79/2.51	----------------------------------------
4.79/2.51	
4.79/2.51	(3) TerminationGraphProcessor (SOUND)
4.79/2.51	Constructed the termination graph and obtained one non-trivial SCC.
4.79/2.51	
4.79/2.51	----------------------------------------
4.79/2.51	
4.79/2.51	(4)
4.79/2.51	Obligation:
4.79/2.51	Rules:
4.79/2.51	f4(x21, x22, x23) -> f5(x21, x22, x23) :|: x21 - x22 > 0
4.79/2.51	f9(x24, x25, x26) -> f4(x24, x25, x26) :|: TRUE
4.79/2.51	f8(x30, x31, x32) -> f9(x30, x31, x33) :|: TRUE && x33 = x32 + 1
4.79/2.51	f7(x15, x16, x17) -> f8(x15, x16, x17) :|: TRUE
4.79/2.51	f6(x12, x13, x14) -> f7(x12, x14, x14) :|: TRUE
4.79/2.51	f5(x9, x10, x11) -> f6(arith, x10, x11) :|: TRUE && arith = 0 - x9 + x10
4.79/2.51	
4.79/2.51	----------------------------------------
4.79/2.51	
4.79/2.51	(5) IntTRSCompressionProof (EQUIVALENT)
4.79/2.51	Compressed rules.
4.79/2.51	----------------------------------------
4.79/2.51	
4.79/2.51	(6)
4.79/2.51	Obligation:
4.79/2.51	Rules:
4.79/2.51	f6(x12:0, x13:0, x14:0) -> f6(0 - x12:0 + x14:0, x14:0, x14:0 + 1) :|: x12:0 - x14:0 > 0
4.79/2.51	
4.79/2.51	----------------------------------------
4.79/2.51	
4.79/2.51	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.79/2.51	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.79/2.51	
4.79/2.51	   f6(x1, x2, x3) -> f6(x1, x3)
4.79/2.51	
4.79/2.51	----------------------------------------
4.79/2.51	
4.79/2.51	(8)
4.79/2.51	Obligation:
4.79/2.51	Rules:
4.79/2.51	f6(x12:0, x14:0) -> f6(0 - x12:0 + x14:0, x14:0 + 1) :|: x12:0 - x14:0 > 0
4.79/2.51	
4.79/2.51	----------------------------------------
4.79/2.51	
4.79/2.51	(9) PolynomialOrderProcessor (EQUIVALENT)
4.79/2.51	Found the following polynomial interpretation:
4.79/2.51	[f6(x, x1)] = -2 + 2*x - 2*x1 + x1^2
4.79/2.51	
4.79/2.51	The following rules are decreasing:
4.79/2.51	f6(x12:0, x14:0) -> f6(0 - x12:0 + x14:0, x14:0 + 1) :|: x12:0 - x14:0 > 0
4.79/2.51	The following rules are bounded:
4.79/2.51	f6(x12:0, x14:0) -> f6(0 - x12:0 + x14:0, x14:0 + 1) :|: x12:0 - x14:0 > 0
4.79/2.51	
4.79/2.51	----------------------------------------
4.79/2.51	
4.79/2.51	(10)
4.79/2.51	YES
5.09/2.54	EOF