4.91/2.01	YES
4.91/2.02	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.91/2.02	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.91/2.02	
4.91/2.02	
4.91/2.02	Termination of the given C Problem could be proven:
4.91/2.02	
4.91/2.02	(0) C Problem
4.91/2.02	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.91/2.02	(2) IntTRS
4.91/2.02	(3) TerminationGraphProcessor [SOUND, 46 ms]
4.91/2.02	(4) IntTRS
4.91/2.02	(5) IntTRSCompressionProof [EQUIVALENT, 9 ms]
4.91/2.02	(6) IntTRS
4.91/2.02	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.91/2.02	(8) IntTRS
4.91/2.02	(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
4.91/2.02	(10) YES
4.91/2.02	
4.91/2.02	
4.91/2.02	----------------------------------------
4.91/2.02	
4.91/2.02	(0)
4.91/2.02	Obligation:
4.91/2.02	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.91/2.02	----------------------------------------
4.91/2.02	
4.91/2.02	(1) CToIRSProof (EQUIVALENT)
4.91/2.02	Parsed C Integer Program as IRS.
4.91/2.02	----------------------------------------
4.91/2.02	
4.91/2.02	(2)
4.91/2.02	Obligation:
4.91/2.02	Rules:
4.91/2.02	f1(c, x, y) -> f2(c, x_1, y) :|: TRUE
4.91/2.02	f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE
4.91/2.02	f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE
4.91/2.02	f5(x8, x9, x10) -> f6(x8, x9, arith) :|: TRUE && arith = x10 + 1
4.91/2.02	f6(x23, x24, x25) -> f7(x26, x24, x25) :|: TRUE && x26 = x23 + 1
4.91/2.02	f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x15 > x16
4.91/2.02	f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE
4.91/2.02	f4(x20, x21, x22) -> f8(x20, x21, x22) :|: x21 <= x22
4.91/2.02	Start term: f1(c, x, y)
4.91/2.02	
4.91/2.02	----------------------------------------
4.91/2.02	
4.91/2.02	(3) TerminationGraphProcessor (SOUND)
4.91/2.02	Constructed the termination graph and obtained one non-trivial SCC.
4.91/2.02	
4.91/2.02	----------------------------------------
4.91/2.02	
4.91/2.02	(4)
4.91/2.02	Obligation:
4.91/2.02	Rules:
4.91/2.02	f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x15 > x16
4.91/2.02	f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE
4.91/2.02	f6(x23, x24, x25) -> f7(x26, x24, x25) :|: TRUE && x26 = x23 + 1
4.91/2.02	f5(x8, x9, x10) -> f6(x8, x9, arith) :|: TRUE && arith = x10 + 1
4.91/2.02	
4.91/2.02	----------------------------------------
4.91/2.02	
4.91/2.02	(5) IntTRSCompressionProof (EQUIVALENT)
4.91/2.02	Compressed rules.
4.91/2.02	----------------------------------------
4.91/2.02	
4.91/2.02	(6)
4.91/2.02	Obligation:
4.91/2.02	Rules:
4.91/2.02	f6(x23:0, x24:0, x25:0) -> f6(x23:0 + 1, x24:0, x25:0 + 1) :|: x25:0 < x24:0
4.91/2.02	
4.91/2.02	----------------------------------------
4.91/2.02	
4.91/2.02	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.91/2.02	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.91/2.02	
4.91/2.02	   f6(x1, x2, x3) -> f6(x2, x3)
4.91/2.02	
4.91/2.02	----------------------------------------
4.91/2.02	
4.91/2.02	(8)
4.91/2.02	Obligation:
4.91/2.02	Rules:
4.91/2.02	f6(x24:0, x25:0) -> f6(x24:0, x25:0 + 1) :|: x25:0 < x24:0
4.91/2.02	
4.91/2.02	----------------------------------------
4.91/2.02	
4.91/2.02	(9) PolynomialOrderProcessor (EQUIVALENT)
4.91/2.02	Found the following polynomial interpretation:
4.91/2.02	[f6(x, x1)] = x - x1
4.91/2.02	
4.91/2.02	The following rules are decreasing:
4.91/2.02	f6(x24:0, x25:0) -> f6(x24:0, x25:0 + 1) :|: x25:0 < x24:0
4.91/2.02	The following rules are bounded:
4.91/2.02	f6(x24:0, x25:0) -> f6(x24:0, x25:0 + 1) :|: x25:0 < x24:0
4.91/2.02	
4.91/2.02	----------------------------------------
4.91/2.02	
4.91/2.02	(10)
4.91/2.02	YES
4.91/2.06	EOF