7.26/2.66	YES
7.26/2.68	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
7.26/2.68	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
7.26/2.68	
7.26/2.68	
7.26/2.68	Termination of the given C Problem could be proven:
7.26/2.68	
7.26/2.68	(0) C Problem
7.26/2.68	(1) CToIRSProof [EQUIVALENT, 0 ms]
7.26/2.68	(2) IntTRS
7.26/2.68	(3) TerminationGraphProcessor [SOUND, 50 ms]
7.26/2.68	(4) IntTRS
7.26/2.68	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
7.26/2.68	(6) IntTRS
7.26/2.68	(7) PolynomialOrderProcessor [EQUIVALENT, 10 ms]
7.26/2.68	(8) AND
7.26/2.68	    (9) IntTRS
7.26/2.68	        (10) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
7.26/2.68	        (11) YES
7.26/2.68	    (12) IntTRS
7.26/2.68	        (13) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
7.26/2.68	        (14) YES
7.26/2.68	
7.26/2.68	
7.26/2.68	----------------------------------------
7.26/2.68	
7.26/2.68	(0)
7.26/2.68	Obligation:
7.26/2.68	c file /export/starexec/sandbox/benchmark/theBenchmark.c
7.26/2.68	----------------------------------------
7.26/2.68	
7.26/2.68	(1) CToIRSProof (EQUIVALENT)
7.26/2.68	Parsed C Integer Program as IRS.
7.26/2.68	----------------------------------------
7.26/2.68	
7.26/2.68	(2)
7.26/2.68	Obligation:
7.26/2.68	Rules:
7.26/2.68	f1(x, c) -> f2(x_1, c) :|: TRUE
7.26/2.68	f2(x1, x2) -> f3(x1, 1) :|: TRUE
7.26/2.68	f5(x3, x4) -> f8(arith, x4) :|: TRUE && arith = x3 - 10
7.26/2.68	f8(x25, x26) -> f9(x25, x27) :|: TRUE && x27 = x26 - 1
7.26/2.68	f6(x28, x29) -> f10(x30, x29) :|: TRUE && x30 = x28 + 11
7.26/2.68	f10(x31, x32) -> f11(x31, x33) :|: TRUE && x33 = x32 + 1
7.26/2.68	f4(x11, x12) -> f5(x11, x12) :|: x11 > 100
7.26/2.68	f4(x13, x14) -> f6(x13, x14) :|: x13 <= 100
7.26/2.68	f9(x15, x16) -> f7(x15, x16) :|: TRUE
7.26/2.68	f11(x17, x18) -> f7(x17, x18) :|: TRUE
7.26/2.68	f3(x19, x20) -> f4(x19, x20) :|: x20 > 0
7.26/2.68	f7(x21, x22) -> f3(x21, x22) :|: TRUE
7.26/2.68	f3(x23, x24) -> f12(x23, x24) :|: x24 <= 0
7.26/2.68	Start term: f1(x, c)
7.26/2.68	
7.26/2.68	----------------------------------------
7.26/2.68	
7.26/2.68	(3) TerminationGraphProcessor (SOUND)
7.26/2.68	Constructed the termination graph and obtained one non-trivial SCC.
7.26/2.68	
7.26/2.68	----------------------------------------
7.26/2.68	
7.26/2.68	(4)
7.26/2.68	Obligation:
7.26/2.68	Rules:
7.26/2.68	f3(x19, x20) -> f4(x19, x20) :|: x20 > 0
7.26/2.68	f7(x21, x22) -> f3(x21, x22) :|: TRUE
7.26/2.68	f9(x15, x16) -> f7(x15, x16) :|: TRUE
7.26/2.68	f8(x25, x26) -> f9(x25, x27) :|: TRUE && x27 = x26 - 1
7.26/2.68	f5(x3, x4) -> f8(arith, x4) :|: TRUE && arith = x3 - 10
7.26/2.68	f4(x11, x12) -> f5(x11, x12) :|: x11 > 100
7.26/2.68	f11(x17, x18) -> f7(x17, x18) :|: TRUE
7.26/2.68	f10(x31, x32) -> f11(x31, x33) :|: TRUE && x33 = x32 + 1
7.26/2.68	f6(x28, x29) -> f10(x30, x29) :|: TRUE && x30 = x28 + 11
7.26/2.68	f4(x13, x14) -> f6(x13, x14) :|: x13 <= 100
7.26/2.68	
7.26/2.68	----------------------------------------
7.26/2.68	
7.26/2.68	(5) IntTRSCompressionProof (EQUIVALENT)
7.26/2.68	Compressed rules.
7.26/2.68	----------------------------------------
7.26/2.68	
7.26/2.68	(6)
7.26/2.68	Obligation:
7.26/2.68	Rules:
7.26/2.68	f7(x21:0, x22:0) -> f7(x21:0 - 10, x22:0 - 1) :|: x22:0 > 0 && x21:0 > 100
7.26/2.68	f7(x, x1) -> f7(x + 11, x1 + 1) :|: x1 > 0 && x < 101
7.26/2.68	
7.26/2.68	----------------------------------------
7.26/2.68	
7.26/2.68	(7) PolynomialOrderProcessor (EQUIVALENT)
7.26/2.68	Found the following polynomial interpretation:
7.26/2.68	[f7(x, x1)] = 89 - x + 11*x1
7.26/2.68	
7.26/2.68	The following rules are decreasing:
7.26/2.68	f7(x21:0, x22:0) -> f7(x21:0 - 10, x22:0 - 1) :|: x22:0 > 0 && x21:0 > 100
7.26/2.68	The following rules are bounded:
7.26/2.68	f7(x, x1) -> f7(x + 11, x1 + 1) :|: x1 > 0 && x < 101
7.26/2.68	
7.26/2.68	----------------------------------------
7.26/2.68	
7.26/2.68	(8)
7.26/2.68	Complex Obligation (AND)
7.26/2.68	
7.26/2.68	----------------------------------------
7.26/2.68	
7.26/2.68	(9)
7.26/2.68	Obligation:
7.26/2.68	Rules:
7.26/2.68	f7(x, x1) -> f7(x + 11, x1 + 1) :|: x1 > 0 && x < 101
7.26/2.68	
7.26/2.68	----------------------------------------
7.26/2.68	
7.26/2.68	(10) PolynomialOrderProcessor (EQUIVALENT)
7.26/2.68	Found the following polynomial interpretation:
7.26/2.68	[f7(x, x1)] = 90 - x + 10*x1
7.26/2.68	
7.26/2.68	The following rules are decreasing:
7.26/2.68	f7(x, x1) -> f7(x + 11, x1 + 1) :|: x1 > 0 && x < 101
7.26/2.68	The following rules are bounded:
7.26/2.68	f7(x, x1) -> f7(x + 11, x1 + 1) :|: x1 > 0 && x < 101
7.26/2.68	
7.26/2.68	----------------------------------------
7.26/2.68	
7.26/2.68	(11)
7.26/2.68	YES
7.26/2.68	
7.26/2.68	----------------------------------------
7.26/2.68	
7.26/2.68	(12)
7.26/2.68	Obligation:
7.26/2.68	Rules:
7.26/2.68	f7(x21:0, x22:0) -> f7(x21:0 - 10, x22:0 - 1) :|: x22:0 > 0 && x21:0 > 100
7.26/2.68	
7.26/2.68	----------------------------------------
7.26/2.68	
7.26/2.68	(13) PolynomialOrderProcessor (EQUIVALENT)
7.26/2.68	Found the following polynomial interpretation:
7.26/2.68	[f7(x, x1)] = x1
7.26/2.68	
7.26/2.68	The following rules are decreasing:
7.26/2.68	f7(x21:0, x22:0) -> f7(x21:0 - 10, x22:0 - 1) :|: x22:0 > 0 && x21:0 > 100
7.26/2.68	The following rules are bounded:
7.26/2.68	f7(x21:0, x22:0) -> f7(x21:0 - 10, x22:0 - 1) :|: x22:0 > 0 && x21:0 > 100
7.26/2.68	
7.26/2.68	----------------------------------------
7.26/2.68	
7.26/2.68	(14)
7.26/2.68	YES
7.46/2.78	EOF