5.19/2.12	YES
5.19/2.13	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
5.19/2.13	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.19/2.13	
5.19/2.13	
5.19/2.13	Termination of the given C Problem could be proven:
5.19/2.13	
5.19/2.13	(0) C Problem
5.19/2.13	(1) CToIRSProof [EQUIVALENT, 0 ms]
5.19/2.13	(2) IntTRS
5.19/2.13	(3) TerminationGraphProcessor [SOUND, 57 ms]
5.19/2.13	(4) IntTRS
5.19/2.13	(5) IntTRSCompressionProof [EQUIVALENT, 26 ms]
5.19/2.13	(6) IntTRS
5.19/2.13	(7) PolynomialOrderProcessor [EQUIVALENT, 12 ms]
5.19/2.13	(8) AND
5.19/2.13	    (9) IntTRS
5.19/2.13	        (10) TerminationGraphProcessor [EQUIVALENT, 0 ms]
5.19/2.13	        (11) YES
5.19/2.13	    (12) IntTRS
5.19/2.13	        (13) TerminationGraphProcessor [EQUIVALENT, 3 ms]
5.19/2.13	        (14) YES
5.19/2.13	
5.19/2.13	
5.19/2.13	----------------------------------------
5.19/2.13	
5.19/2.13	(0)
5.19/2.13	Obligation:
5.19/2.13	c file /export/starexec/sandbox/benchmark/theBenchmark.c
5.19/2.13	----------------------------------------
5.19/2.13	
5.19/2.13	(1) CToIRSProof (EQUIVALENT)
5.19/2.13	Parsed C Integer Program as IRS.
5.19/2.13	----------------------------------------
5.19/2.13	
5.19/2.13	(2)
5.19/2.13	Obligation:
5.19/2.13	Rules:
5.19/2.13	f1(a, b) -> f2(x_1, b) :|: TRUE
5.19/2.13	f2(x, x1) -> f3(x, x2) :|: TRUE
5.19/2.13	f4(x3, x4) -> f5(arith, x4) :|: TRUE && arith = x3 + x4
5.19/2.13	f6(x23, x24) -> f9(x23, x25) :|: TRUE && x25 = 0 - x24 - 1
5.19/2.13	f7(x26, x27) -> f10(x26, x28) :|: TRUE && x28 = 0 - x27
5.19/2.13	f5(x9, x10) -> f6(x9, x10) :|: x10 >= 0
5.19/2.13	f5(x11, x12) -> f7(x11, x12) :|: x12 < 0
5.19/2.13	f9(x13, x14) -> f8(x13, x14) :|: TRUE
5.19/2.13	f10(x15, x16) -> f8(x15, x16) :|: TRUE
5.19/2.13	f3(x17, x18) -> f4(x17, x18) :|: x17 >= 0
5.19/2.13	f8(x19, x20) -> f3(x19, x20) :|: TRUE
5.19/2.13	f3(x21, x22) -> f11(x21, x22) :|: x21 < 0
5.19/2.13	Start term: f1(a, b)
5.19/2.13	
5.19/2.13	----------------------------------------
5.19/2.13	
5.19/2.13	(3) TerminationGraphProcessor (SOUND)
5.19/2.13	Constructed the termination graph and obtained one non-trivial SCC.
5.19/2.13	
5.19/2.13	----------------------------------------
5.19/2.13	
5.19/2.13	(4)
5.19/2.13	Obligation:
5.19/2.13	Rules:
5.19/2.13	f3(x17, x18) -> f4(x17, x18) :|: x17 >= 0
5.19/2.13	f8(x19, x20) -> f3(x19, x20) :|: TRUE
5.19/2.13	f9(x13, x14) -> f8(x13, x14) :|: TRUE
5.19/2.13	f6(x23, x24) -> f9(x23, x25) :|: TRUE && x25 = 0 - x24 - 1
5.19/2.13	f5(x9, x10) -> f6(x9, x10) :|: x10 >= 0
5.19/2.13	f4(x3, x4) -> f5(arith, x4) :|: TRUE && arith = x3 + x4
5.19/2.13	f10(x15, x16) -> f8(x15, x16) :|: TRUE
5.19/2.13	f7(x26, x27) -> f10(x26, x28) :|: TRUE && x28 = 0 - x27
5.19/2.13	f5(x11, x12) -> f7(x11, x12) :|: x12 < 0
5.19/2.13	
5.19/2.13	----------------------------------------
5.19/2.13	
5.19/2.13	(5) IntTRSCompressionProof (EQUIVALENT)
5.19/2.13	Compressed rules.
5.19/2.13	----------------------------------------
5.19/2.13	
5.19/2.13	(6)
5.19/2.13	Obligation:
5.19/2.13	Rules:
5.19/2.13	f5(x9:0, x10:0) -> f5(x9:0 + (0 - x10:0 - 1), 0 - x10:0 - 1) :|: x10:0 > -1 && x9:0 > -1
5.19/2.13	f5(x11:0, x12:0) -> f5(x11:0 + (0 - x12:0), 0 - x12:0) :|: x12:0 < 0 && x11:0 > -1
5.19/2.13	
5.19/2.13	----------------------------------------
5.19/2.13	
5.19/2.13	(7) PolynomialOrderProcessor (EQUIVALENT)
5.19/2.13	Found the following polynomial interpretation:
5.19/2.13	[f5(x, x1)] = -1 + 2*x - x1
5.19/2.13	
5.19/2.13	The following rules are decreasing:
5.19/2.13	f5(x9:0, x10:0) -> f5(x9:0 + (0 - x10:0 - 1), 0 - x10:0 - 1) :|: x10:0 > -1 && x9:0 > -1
5.19/2.13	The following rules are bounded:
5.19/2.13	f5(x11:0, x12:0) -> f5(x11:0 + (0 - x12:0), 0 - x12:0) :|: x12:0 < 0 && x11:0 > -1
5.19/2.13	
5.19/2.13	----------------------------------------
5.19/2.13	
5.19/2.13	(8)
5.19/2.13	Complex Obligation (AND)
5.19/2.13	
5.19/2.13	----------------------------------------
5.19/2.13	
5.19/2.13	(9)
5.19/2.13	Obligation:
5.19/2.13	Rules:
5.19/2.13	f5(x11:0, x12:0) -> f5(x11:0 + (0 - x12:0), 0 - x12:0) :|: x12:0 < 0 && x11:0 > -1
5.19/2.13	
5.19/2.13	----------------------------------------
5.19/2.13	
5.19/2.13	(10) TerminationGraphProcessor (EQUIVALENT)
5.19/2.13	Constructed the termination graph and obtained no non-trivial SCC(s).
5.19/2.13	
5.19/2.13	----------------------------------------
5.19/2.13	
5.19/2.13	(11)
5.19/2.13	YES
5.19/2.13	
5.19/2.13	----------------------------------------
5.19/2.13	
5.19/2.13	(12)
5.19/2.13	Obligation:
5.19/2.13	Rules:
5.19/2.13	f5(x9:0, x10:0) -> f5(x9:0 + (0 - x10:0 - 1), 0 - x10:0 - 1) :|: x10:0 > -1 && x9:0 > -1
5.19/2.13	
5.19/2.13	----------------------------------------
5.19/2.13	
5.19/2.13	(13) TerminationGraphProcessor (EQUIVALENT)
5.19/2.13	Constructed the termination graph and obtained no non-trivial SCC(s).
5.19/2.13	
5.19/2.13	----------------------------------------
5.19/2.13	
5.19/2.13	(14)
5.19/2.13	YES
5.48/2.17	EOF