4.58/2.20	YES
4.58/2.21	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.58/2.21	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.58/2.21	
4.58/2.21	
4.58/2.21	Termination of the given C Problem could be proven:
4.58/2.21	
4.58/2.21	(0) C Problem
4.58/2.21	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.58/2.21	(2) IntTRS
4.58/2.21	(3) TerminationGraphProcessor [SOUND, 34 ms]
4.58/2.21	(4) IntTRS
4.58/2.21	(5) IntTRSCompressionProof [EQUIVALENT, 4 ms]
4.58/2.21	(6) IntTRS
4.58/2.21	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.58/2.21	(8) IntTRS
4.58/2.21	(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
4.58/2.21	(10) YES
4.58/2.21	
4.58/2.21	
4.58/2.21	----------------------------------------
4.58/2.21	
4.58/2.21	(0)
4.58/2.21	Obligation:
4.58/2.21	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.58/2.21	----------------------------------------
4.58/2.21	
4.58/2.21	(1) CToIRSProof (EQUIVALENT)
4.58/2.21	Parsed C Integer Program as IRS.
4.58/2.21	----------------------------------------
4.58/2.21	
4.58/2.21	(2)
4.58/2.21	Obligation:
4.58/2.21	Rules:
4.58/2.21	f1(x, y, res) -> f2(x_1, y, res) :|: TRUE
4.58/2.21	f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
4.58/2.21	f3(x5, x6, x7) -> f4(x5, x6, 0) :|: TRUE
4.58/2.21	f5(x8, x9, x10) -> f6(x8, arith, x10) :|: TRUE && arith = x8 + 1
4.58/2.21	f6(x23, x24, x25) -> f7(x23, x24, x26) :|: TRUE && x26 = x25 + 1
4.58/2.21	f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x14 > x15
4.58/2.21	f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE
4.58/2.21	f4(x20, x21, x22) -> f8(x20, x21, x22) :|: x20 <= x21
4.58/2.21	Start term: f1(x, y, res)
4.58/2.21	
4.58/2.21	----------------------------------------
4.58/2.21	
4.58/2.21	(3) TerminationGraphProcessor (SOUND)
4.58/2.21	Constructed the termination graph and obtained one non-trivial SCC.
4.58/2.21	
4.58/2.21	----------------------------------------
4.58/2.21	
4.58/2.21	(4)
4.58/2.21	Obligation:
4.58/2.21	Rules:
4.58/2.21	f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x14 > x15
4.58/2.21	f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE
4.58/2.21	f6(x23, x24, x25) -> f7(x23, x24, x26) :|: TRUE && x26 = x25 + 1
4.58/2.21	f5(x8, x9, x10) -> f6(x8, arith, x10) :|: TRUE && arith = x8 + 1
4.58/2.21	
4.58/2.21	----------------------------------------
4.58/2.21	
4.58/2.21	(5) IntTRSCompressionProof (EQUIVALENT)
4.58/2.21	Compressed rules.
4.58/2.21	----------------------------------------
4.58/2.21	
4.58/2.21	(6)
4.58/2.21	Obligation:
4.58/2.21	Rules:
4.58/2.21	f6(x23:0, x24:0, x25:0) -> f6(x23:0, x23:0 + 1, x25:0 + 1) :|: x24:0 < x23:0
4.58/2.21	
4.58/2.21	----------------------------------------
4.58/2.21	
4.58/2.21	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.58/2.21	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.58/2.21	
4.58/2.21	   f6(x1, x2, x3) -> f6(x1, x2)
4.58/2.21	
4.58/2.21	----------------------------------------
4.58/2.21	
4.58/2.21	(8)
4.58/2.21	Obligation:
4.58/2.21	Rules:
4.58/2.21	f6(x23:0, x24:0) -> f6(x23:0, x23:0 + 1) :|: x24:0 < x23:0
4.58/2.21	
4.58/2.21	----------------------------------------
4.58/2.21	
4.58/2.21	(9) PolynomialOrderProcessor (EQUIVALENT)
4.58/2.21	Found the following polynomial interpretation:
4.58/2.21	[f6(x, x1)] = x - x1
4.58/2.21	
4.58/2.21	The following rules are decreasing:
4.58/2.21	f6(x23:0, x24:0) -> f6(x23:0, x23:0 + 1) :|: x24:0 < x23:0
4.58/2.21	The following rules are bounded:
4.58/2.21	f6(x23:0, x24:0) -> f6(x23:0, x23:0 + 1) :|: x24:0 < x23:0
4.58/2.21	
4.58/2.21	----------------------------------------
4.58/2.21	
4.58/2.21	(10)
4.58/2.21	YES
4.74/2.24	EOF