7.66/2.76	YES
7.66/2.77	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
7.66/2.77	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
7.66/2.77	
7.66/2.77	
7.66/2.77	Termination of the given C Problem could be proven:
7.66/2.77	
7.66/2.77	(0) C Problem
7.66/2.77	(1) CToIRSProof [EQUIVALENT, 0 ms]
7.66/2.77	(2) IntTRS
7.66/2.77	(3) TerminationGraphProcessor [SOUND, 68 ms]
7.66/2.77	(4) IntTRS
7.66/2.77	(5) IntTRSCompressionProof [EQUIVALENT, 30 ms]
7.66/2.77	(6) IntTRS
7.66/2.77	(7) PolynomialOrderProcessor [EQUIVALENT, 15 ms]
7.66/2.77	(8) IntTRS
7.66/2.77	(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
7.66/2.77	(10) IntTRS
7.66/2.77	(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
7.66/2.77	(12) IntTRS
7.66/2.77	(13) PolynomialOrderProcessor [EQUIVALENT, 2 ms]
7.66/2.77	(14) YES
7.66/2.77	
7.66/2.77	
7.66/2.77	----------------------------------------
7.66/2.77	
7.66/2.77	(0)
7.66/2.77	Obligation:
7.66/2.77	c file /export/starexec/sandbox/benchmark/theBenchmark.c
7.66/2.77	----------------------------------------
7.66/2.77	
7.66/2.77	(1) CToIRSProof (EQUIVALENT)
7.66/2.77	Parsed C Integer Program as IRS.
7.66/2.77	----------------------------------------
7.66/2.77	
7.66/2.77	(2)
7.66/2.77	Obligation:
7.66/2.77	Rules:
7.66/2.77	f1(x, y) -> f2(x_1, y) :|: TRUE
7.66/2.77	f2(x1, x2) -> f3(x1, x3) :|: TRUE
7.66/2.77	f5(x4, x5) -> f8(arith, x5) :|: TRUE && arith = x4 - 1
7.66/2.77	f6(x22, x23) -> f9(x22, x24) :|: TRUE && x24 = x23 - 1
7.66/2.77	f4(x8, x9) -> f5(x8, x9) :|: x8 >= 0
7.66/2.77	f4(x10, x11) -> f6(x10, x11) :|: x10 < 0
7.66/2.77	f8(x12, x13) -> f7(x12, x13) :|: TRUE
7.66/2.77	f9(x14, x15) -> f7(x14, x15) :|: TRUE
7.66/2.77	f3(x16, x17) -> f4(x16, x17) :|: x16 >= 0
7.66/2.77	f3(x25, x26) -> f4(x25, x26) :|: x26 >= 0
7.66/2.77	f7(x18, x19) -> f3(x18, x19) :|: TRUE
7.66/2.77	f3(x20, x21) -> f10(x20, x21) :|: x20 < 0 && x21 < 0
7.66/2.77	Start term: f1(x, y)
7.66/2.77	
7.66/2.77	----------------------------------------
7.66/2.77	
7.66/2.77	(3) TerminationGraphProcessor (SOUND)
7.66/2.77	Constructed the termination graph and obtained one non-trivial SCC.
7.66/2.77	
7.66/2.77	----------------------------------------
7.66/2.77	
7.66/2.77	(4)
7.66/2.77	Obligation:
7.66/2.77	Rules:
7.66/2.77	f3(x16, x17) -> f4(x16, x17) :|: x16 >= 0
7.66/2.77	f7(x18, x19) -> f3(x18, x19) :|: TRUE
7.66/2.77	f8(x12, x13) -> f7(x12, x13) :|: TRUE
7.66/2.77	f5(x4, x5) -> f8(arith, x5) :|: TRUE && arith = x4 - 1
7.66/2.77	f4(x8, x9) -> f5(x8, x9) :|: x8 >= 0
7.66/2.77	f3(x25, x26) -> f4(x25, x26) :|: x26 >= 0
7.66/2.77	f9(x14, x15) -> f7(x14, x15) :|: TRUE
7.66/2.77	f6(x22, x23) -> f9(x22, x24) :|: TRUE && x24 = x23 - 1
7.66/2.77	f4(x10, x11) -> f6(x10, x11) :|: x10 < 0
7.66/2.77	
7.66/2.77	----------------------------------------
7.66/2.77	
7.66/2.77	(5) IntTRSCompressionProof (EQUIVALENT)
7.66/2.77	Compressed rules.
7.66/2.77	----------------------------------------
7.66/2.77	
7.66/2.77	(6)
7.66/2.77	Obligation:
7.66/2.77	Rules:
7.66/2.77	f7(x18:0, x19:0) -> f4(x18:0, x19:0) :|: x19:0 > -1
7.66/2.77	f4(x10:0, x11:0) -> f7(x10:0, x11:0 - 1) :|: x10:0 < 0
7.66/2.77	f7(x, x1) -> f4(x, x1) :|: x > -1
7.66/2.77	f4(x8:0, x9:0) -> f7(x8:0 - 1, x9:0) :|: x8:0 > -1
7.66/2.77	
7.66/2.77	----------------------------------------
7.66/2.77	
7.66/2.77	(7) PolynomialOrderProcessor (EQUIVALENT)
7.66/2.77	Found the following polynomial interpretation:
7.66/2.77	[f7(x, x1)] = x
7.66/2.77	[f4(x2, x3)] = x2
7.66/2.77	
7.66/2.77	The following rules are decreasing:
7.66/2.77	f4(x8:0, x9:0) -> f7(x8:0 - 1, x9:0) :|: x8:0 > -1
7.66/2.77	The following rules are bounded:
7.66/2.77	f7(x, x1) -> f4(x, x1) :|: x > -1
7.66/2.77	f4(x8:0, x9:0) -> f7(x8:0 - 1, x9:0) :|: x8:0 > -1
7.66/2.77	
7.66/2.77	----------------------------------------
7.66/2.77	
7.66/2.77	(8)
7.66/2.77	Obligation:
7.66/2.77	Rules:
7.66/2.77	f7(x18:0, x19:0) -> f4(x18:0, x19:0) :|: x19:0 > -1
7.66/2.77	f4(x10:0, x11:0) -> f7(x10:0, x11:0 - 1) :|: x10:0 < 0
7.66/2.77	f7(x, x1) -> f4(x, x1) :|: x > -1
7.66/2.77	
7.66/2.77	----------------------------------------
7.66/2.77	
7.66/2.77	(9) IntTRSCompressionProof (EQUIVALENT)
7.66/2.77	Compressed rules.
7.66/2.77	----------------------------------------
7.66/2.77	
7.66/2.77	(10)
7.66/2.77	Obligation:
7.66/2.77	Rules:
7.66/2.77	f7(x18:0:0, x19:0:0) -> f7(x18:0:0, x19:0:0 - 1) :|: x19:0:0 > -1 && x18:0:0 < 0
7.66/2.77	f7(x:0, x1:0) -> f7(x:0, x1:0 - 1) :|: x:0 > -1 && x:0 < 0
7.66/2.77	
7.66/2.77	----------------------------------------
7.66/2.77	
7.66/2.77	(11) PolynomialOrderProcessor (EQUIVALENT)
7.66/2.77	Found the following polynomial interpretation:
7.66/2.77	[f7(x, x1)] = d + c*x + c1*x^2
7.66/2.77	
7.66/2.77	The following rules are decreasing:
7.66/2.77	f7(x:0, x1:0) -> f7(x:0, x1:0 - 1) :|: x:0 > -1 && x:0 < 0
7.66/2.77	The following rules are bounded:
7.66/2.77	f7(x:0, x1:0) -> f7(x:0, x1:0 - 1) :|: x:0 > -1 && x:0 < 0
7.66/2.77	
7.66/2.77	----------------------------------------
7.66/2.77	
7.66/2.77	(12)
7.66/2.77	Obligation:
7.66/2.77	Rules:
7.66/2.77	f7(x18:0:0, x19:0:0) -> f7(x18:0:0, x19:0:0 - 1) :|: x19:0:0 > -1 && x18:0:0 < 0
7.66/2.77	
7.66/2.77	----------------------------------------
7.66/2.77	
7.66/2.77	(13) PolynomialOrderProcessor (EQUIVALENT)
7.66/2.77	Found the following polynomial interpretation:
7.66/2.77	[f7(x, x1)] = x1
7.66/2.77	
7.66/2.77	The following rules are decreasing:
7.66/2.77	f7(x18:0:0, x19:0:0) -> f7(x18:0:0, x19:0:0 - 1) :|: x19:0:0 > -1 && x18:0:0 < 0
7.66/2.77	The following rules are bounded:
7.66/2.77	f7(x18:0:0, x19:0:0) -> f7(x18:0:0, x19:0:0 - 1) :|: x19:0:0 > -1 && x18:0:0 < 0
7.66/2.77	
7.66/2.77	----------------------------------------
7.66/2.77	
7.66/2.77	(14)
7.66/2.77	YES
7.94/2.83	EOF