6.22/2.47	YES
6.22/2.48	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
6.22/2.48	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.22/2.48	
6.22/2.48	
6.22/2.48	Termination of the given C Problem could be proven:
6.22/2.48	
6.22/2.48	(0) C Problem
6.22/2.48	(1) CToIRSProof [EQUIVALENT, 0 ms]
6.22/2.48	(2) IntTRS
6.22/2.48	(3) TerminationGraphProcessor [SOUND, 61 ms]
6.22/2.48	(4) IntTRS
6.22/2.48	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.22/2.48	(6) IntTRS
6.22/2.48	(7) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
6.22/2.48	(8) IntTRS
6.22/2.48	(9) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
6.22/2.48	(10) IntTRS
6.22/2.48	(11) PolynomialOrderProcessor [EQUIVALENT, 2 ms]
6.22/2.48	(12) YES
6.22/2.48	
6.22/2.48	
6.22/2.48	----------------------------------------
6.22/2.48	
6.22/2.48	(0)
6.22/2.48	Obligation:
6.22/2.48	c file /export/starexec/sandbox/benchmark/theBenchmark.c
6.22/2.48	----------------------------------------
6.22/2.48	
6.22/2.48	(1) CToIRSProof (EQUIVALENT)
6.22/2.48	Parsed C Integer Program as IRS.
6.22/2.48	----------------------------------------
6.22/2.48	
6.22/2.48	(2)
6.22/2.48	Obligation:
6.22/2.48	Rules:
6.22/2.48	f1(x1, x2) -> f2(x_1, x2) :|: TRUE
6.22/2.48	f2(x, x3) -> f3(x, x4) :|: TRUE
6.22/2.48	f4(x5, x6) -> f5(x5, 1000) :|: TRUE
6.22/2.48	f6(x7, x8) -> f7(x7, arith) :|: TRUE && arith = x8 - 1
6.22/2.48	f5(x9, x10) -> f6(x9, x10) :|: x10 > 1
6.22/2.48	f7(x11, x12) -> f5(x11, x12) :|: TRUE
6.22/2.48	f5(x13, x14) -> f8(x13, x14) :|: x14 <= 1
6.22/2.48	f8(x23, x24) -> f9(x25, x24) :|: TRUE && x25 = x23 + 1
6.22/2.48	f3(x17, x18) -> f4(x17, x18) :|: x17 <= 10
6.22/2.48	f9(x19, x20) -> f3(x19, x20) :|: TRUE
6.22/2.48	f3(x21, x22) -> f10(x21, x22) :|: x21 > 10
6.22/2.48	Start term: f1(x1, x2)
6.22/2.48	
6.22/2.48	----------------------------------------
6.22/2.48	
6.22/2.48	(3) TerminationGraphProcessor (SOUND)
6.22/2.48	Constructed the termination graph and obtained one non-trivial SCC.
6.22/2.48	
6.22/2.48	----------------------------------------
6.22/2.48	
6.22/2.48	(4)
6.22/2.48	Obligation:
6.22/2.48	Rules:
6.22/2.48	f3(x17, x18) -> f4(x17, x18) :|: x17 <= 10
6.22/2.48	f9(x19, x20) -> f3(x19, x20) :|: TRUE
6.22/2.48	f8(x23, x24) -> f9(x25, x24) :|: TRUE && x25 = x23 + 1
6.22/2.48	f5(x13, x14) -> f8(x13, x14) :|: x14 <= 1
6.22/2.48	f7(x11, x12) -> f5(x11, x12) :|: TRUE
6.22/2.48	f6(x7, x8) -> f7(x7, arith) :|: TRUE && arith = x8 - 1
6.22/2.48	f5(x9, x10) -> f6(x9, x10) :|: x10 > 1
6.22/2.48	f4(x5, x6) -> f5(x5, 1000) :|: TRUE
6.22/2.48	
6.22/2.48	----------------------------------------
6.22/2.48	
6.22/2.48	(5) IntTRSCompressionProof (EQUIVALENT)
6.22/2.48	Compressed rules.
6.22/2.48	----------------------------------------
6.22/2.48	
6.22/2.48	(6)
6.22/2.48	Obligation:
6.22/2.48	Rules:
6.22/2.48	f5(x13:0, x14:0) -> f5(x13:0 + 1, 1000) :|: x14:0 < 2 && x13:0 < 10
6.22/2.48	f5(x9:0, x10:0) -> f5(x9:0, x10:0 - 1) :|: x10:0 > 1
6.22/2.48	
6.22/2.48	----------------------------------------
6.22/2.48	
6.22/2.48	(7) PolynomialOrderProcessor (EQUIVALENT)
6.22/2.48	Found the following polynomial interpretation:
6.22/2.48	[f5(x, x1)] = 9 - x
6.22/2.48	
6.22/2.48	The following rules are decreasing:
6.22/2.48	f5(x13:0, x14:0) -> f5(x13:0 + 1, 1000) :|: x14:0 < 2 && x13:0 < 10
6.22/2.48	The following rules are bounded:
6.22/2.48	f5(x13:0, x14:0) -> f5(x13:0 + 1, 1000) :|: x14:0 < 2 && x13:0 < 10
6.22/2.48	
6.22/2.48	----------------------------------------
6.22/2.48	
6.22/2.48	(8)
6.22/2.48	Obligation:
6.22/2.48	Rules:
6.22/2.48	f5(x9:0, x10:0) -> f5(x9:0, x10:0 - 1) :|: x10:0 > 1
6.22/2.48	
6.22/2.48	----------------------------------------
6.22/2.48	
6.22/2.48	(9) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
6.22/2.48	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
6.22/2.48	
6.22/2.48	   f5(x1, x2) -> f5(x2)
6.22/2.48	
6.22/2.48	----------------------------------------
6.22/2.48	
6.22/2.48	(10)
6.22/2.48	Obligation:
6.22/2.48	Rules:
6.22/2.48	f5(x10:0) -> f5(x10:0 - 1) :|: x10:0 > 1
6.22/2.48	
6.22/2.48	----------------------------------------
6.22/2.48	
6.22/2.48	(11) PolynomialOrderProcessor (EQUIVALENT)
6.22/2.48	Found the following polynomial interpretation:
6.22/2.48	[f5(x)] = x
6.22/2.48	
6.22/2.48	The following rules are decreasing:
6.22/2.48	f5(x10:0) -> f5(x10:0 - 1) :|: x10:0 > 1
6.22/2.48	The following rules are bounded:
6.22/2.48	f5(x10:0) -> f5(x10:0 - 1) :|: x10:0 > 1
6.22/2.48	
6.22/2.48	----------------------------------------
6.22/2.48	
6.22/2.48	(12)
6.22/2.48	YES
6.49/2.50	EOF