6.18/2.38	YES
6.18/2.40	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
6.18/2.40	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.18/2.40	
6.18/2.40	
6.18/2.40	Termination of the given C Problem could be proven:
6.18/2.40	
6.18/2.40	(0) C Problem
6.18/2.40	(1) CToIRSProof [EQUIVALENT, 0 ms]
6.18/2.40	(2) IntTRS
6.18/2.40	(3) TerminationGraphProcessor [SOUND, 28 ms]
6.18/2.40	(4) IntTRS
6.18/2.40	(5) IntTRSCompressionProof [EQUIVALENT, 2 ms]
6.18/2.40	(6) IntTRS
6.18/2.40	(7) TerminationGraphProcessor [EQUIVALENT, 21 ms]
6.18/2.40	(8) IntTRS
6.18/2.40	(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.18/2.40	(10) IntTRS
6.18/2.40	(11) PolynomialOrderProcessor [EQUIVALENT, 7 ms]
6.18/2.40	(12) YES
6.18/2.40	
6.18/2.40	
6.18/2.40	----------------------------------------
6.18/2.40	
6.18/2.40	(0)
6.18/2.40	Obligation:
6.18/2.40	c file /export/starexec/sandbox/benchmark/theBenchmark.c
6.18/2.40	----------------------------------------
6.18/2.40	
6.18/2.40	(1) CToIRSProof (EQUIVALENT)
6.18/2.40	Parsed C Integer Program as IRS.
6.18/2.40	----------------------------------------
6.18/2.40	
6.18/2.40	(2)
6.18/2.40	Obligation:
6.18/2.40	Rules:
6.18/2.40	f1(a, b) -> f2(arith, b) :|: TRUE && arith = 0 - x_1
6.18/2.40	f2(x13, x14) -> f3(x13, x15) :|: TRUE && x15 = 0 - x16
6.18/2.40	f4(x17, x18) -> f5(x17, x19) :|: TRUE && x19 = x18 + x17
6.18/2.40	f5(x20, x21) -> f6(x22, x21) :|: TRUE && x22 = x20 + 1
6.18/2.40	f3(x7, x8) -> f4(x7, x8) :|: x7 > x8
6.18/2.40	f6(x9, x10) -> f3(x9, x10) :|: TRUE
6.18/2.40	f3(x11, x12) -> f7(x11, x12) :|: x11 <= x12
6.18/2.40	Start term: f1(a, b)
6.18/2.40	
6.18/2.40	----------------------------------------
6.18/2.40	
6.18/2.40	(3) TerminationGraphProcessor (SOUND)
6.18/2.40	Constructed the termination graph and obtained one non-trivial SCC.
6.18/2.40	
6.18/2.40	----------------------------------------
6.18/2.40	
6.18/2.40	(4)
6.18/2.40	Obligation:
6.18/2.40	Rules:
6.18/2.40	f3(x7, x8) -> f4(x7, x8) :|: x7 > x8
6.18/2.40	f6(x9, x10) -> f3(x9, x10) :|: TRUE
6.18/2.40	f5(x20, x21) -> f6(x22, x21) :|: TRUE && x22 = x20 + 1
6.18/2.40	f4(x17, x18) -> f5(x17, x19) :|: TRUE && x19 = x18 + x17
6.18/2.40	
6.18/2.40	----------------------------------------
6.18/2.40	
6.18/2.40	(5) IntTRSCompressionProof (EQUIVALENT)
6.18/2.40	Compressed rules.
6.18/2.40	----------------------------------------
6.18/2.40	
6.18/2.40	(6)
6.18/2.40	Obligation:
6.18/2.40	Rules:
6.18/2.40	f5(x20:0, x21:0) -> f5(x20:0 + 1, x21:0 + (x20:0 + 1)) :|: x21:0 < x20:0 + 1
6.18/2.40	
6.18/2.40	----------------------------------------
6.18/2.40	
6.18/2.40	(7) TerminationGraphProcessor (EQUIVALENT)
6.18/2.40	Constructed the termination graph and obtained one non-trivial SCC.
6.18/2.40	
6.18/2.40	f5(x20:0, x21:0) -> f5(x20:0 + 1, x21:0 + (x20:0 + 1)) :|: x21:0 < x20:0 + 1
6.18/2.40	has been transformed into
6.18/2.40	f5(x20:0, x21:0) -> f5(x20:0 + 1, x21:0 + (x20:0 + 1)) :|: x21:0 = x5 + (x4 + 1) && (x20:0 = x4 + 1 && x21:0 < x20:0 + 1) && x5 < x4 + 1.
6.18/2.40	
6.18/2.40	
6.18/2.40	f5(x20:0, x21:0) -> f5(x20:0 + 1, x21:0 + (x20:0 + 1)) :|: x21:0 = x5 + (x4 + 1) && (x20:0 = x4 + 1 && x21:0 < x20:0 + 1) && x5 < x4 + 1 and 
6.18/2.40	f5(x20:0, x21:0) -> f5(x20:0 + 1, x21:0 + (x20:0 + 1)) :|: x21:0 = x5 + (x4 + 1) && (x20:0 = x4 + 1 && x21:0 < x20:0 + 1) && x5 < x4 + 1
6.18/2.40	have been merged into the new rule
6.18/2.40	f5(x14, x15) -> f5(x14 + 1 + 1, x15 + (x14 + 1) + (x14 + 1 + 1)) :|: x15 = x16 + (x17 + 1) && (x14 = x17 + 1 && x15 < x14 + 1) && x16 < x17 + 1 && (x15 + (x14 + 1) = x18 + (x19 + 1) && (x14 + 1 = x19 + 1 && x15 + (x14 + 1) < x14 + 1 + 1) && x18 < x19 + 1)
6.18/2.40	
6.18/2.40	
6.18/2.40	----------------------------------------
6.18/2.40	
6.18/2.40	(8)
6.18/2.40	Obligation:
6.18/2.40	Rules:
6.18/2.40	f5(x20, x21) -> f5(x20 + 2, x21 + 2 * x20 + 3) :|: TRUE && x21 + -1 * x22 + -1 * x23 = 1 && x20 + -1 * x23 = 1 && x21 + -1 * x20 <= 0 && x22 + -1 * x23 <= 0 && x21 + x20 + -1 * x24 + -1 * x25 = 0 && x20 + -1 * x25 = 0 && x21 <= 0 && x24 + -1 * x25 <= 0
6.18/2.40	
6.18/2.40	----------------------------------------
6.18/2.40	
6.18/2.40	(9) IntTRSCompressionProof (EQUIVALENT)
6.18/2.40	Compressed rules.
6.18/2.40	----------------------------------------
6.18/2.40	
6.18/2.40	(10)
6.18/2.40	Obligation:
6.18/2.40	Rules:
6.18/2.40	f5(x20:0, x21:0) -> f5(x20:0 + 2, x21:0 + 2 * x20:0 + 3) :|: x21:0 < 1 && x24:0 + -1 * x25:0 <= 0 && x20:0 + -1 * x25:0 = 0 && x21:0 + x20:0 + -1 * x24:0 + -1 * x25:0 = 0 && x22:0 + -1 * x23:0 <= 0 && x21:0 + -1 * x20:0 <= 0 && x21:0 + -1 * x22:0 + -1 * x23:0 = 1 && x20:0 + -1 * x23:0 = 1
6.18/2.40	
6.18/2.40	----------------------------------------
6.18/2.40	
6.18/2.40	(11) PolynomialOrderProcessor (EQUIVALENT)
6.18/2.40	Found the following polynomial interpretation:
6.18/2.40	[f5(x, x1)] = x^2 - 2*x1
6.18/2.40	
6.18/2.40	The following rules are decreasing:
6.18/2.40	f5(x20:0, x21:0) -> f5(x20:0 + 2, x21:0 + 2 * x20:0 + 3) :|: x21:0 < 1 && x24:0 + -1 * x25:0 <= 0 && x20:0 + -1 * x25:0 = 0 && x21:0 + x20:0 + -1 * x24:0 + -1 * x25:0 = 0 && x22:0 + -1 * x23:0 <= 0 && x21:0 + -1 * x20:0 <= 0 && x21:0 + -1 * x22:0 + -1 * x23:0 = 1 && x20:0 + -1 * x23:0 = 1
6.18/2.40	The following rules are bounded:
6.18/2.40	f5(x20:0, x21:0) -> f5(x20:0 + 2, x21:0 + 2 * x20:0 + 3) :|: x21:0 < 1 && x24:0 + -1 * x25:0 <= 0 && x20:0 + -1 * x25:0 = 0 && x21:0 + x20:0 + -1 * x24:0 + -1 * x25:0 = 0 && x22:0 + -1 * x23:0 <= 0 && x21:0 + -1 * x20:0 <= 0 && x21:0 + -1 * x22:0 + -1 * x23:0 = 1 && x20:0 + -1 * x23:0 = 1
6.18/2.40	
6.18/2.40	----------------------------------------
6.18/2.40	
6.18/2.40	(12)
6.18/2.40	YES
6.45/2.43	EOF