7.80/2.77	YES
7.80/2.78	proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
7.80/2.78	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
7.80/2.78	
7.80/2.78	
7.80/2.78	Termination of the given C Problem could be proven:
7.80/2.78	
7.80/2.78	(0) C Problem
7.80/2.78	(1) CToIRSProof [EQUIVALENT, 0 ms]
7.80/2.78	(2) IntTRS
7.80/2.78	(3) TerminationGraphProcessor [SOUND, 60 ms]
7.80/2.78	(4) IntTRS
7.80/2.78	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
7.80/2.78	(6) IntTRS
7.80/2.78	(7) PolynomialOrderProcessor [EQUIVALENT, 1 ms]
7.80/2.78	(8) AND
7.80/2.78	    (9) IntTRS
7.80/2.78	        (10) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
7.80/2.78	        (11) YES
7.80/2.78	    (12) IntTRS
7.80/2.78	        (13) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
7.80/2.78	        (14) YES
7.80/2.78	
7.80/2.78	
7.80/2.78	----------------------------------------
7.80/2.78	
7.80/2.78	(0)
7.80/2.78	Obligation:
7.80/2.78	c file /export/starexec/sandbox2/benchmark/theBenchmark.c
7.80/2.78	----------------------------------------
7.80/2.78	
7.80/2.78	(1) CToIRSProof (EQUIVALENT)
7.80/2.78	Parsed C Integer Program as IRS.
7.80/2.78	----------------------------------------
7.80/2.78	
7.80/2.78	(2)
7.80/2.78	Obligation:
7.80/2.78	Rules:
7.80/2.78	f1(x, y) -> f2(0, y) :|: TRUE
7.80/2.78	f2(x1, x2) -> f3(x1, 0) :|: TRUE
7.80/2.78	f5(x3, x4) -> f8(x3, arith) :|: TRUE && arith = x4 + 1
7.80/2.78	f6(x23, x24) -> f9(x23, x25) :|: TRUE && x25 = x24 - 1
7.80/2.78	f4(x7, x8) -> f5(x7, x8) :|: x7 <= 50
7.80/2.78	f4(x9, x10) -> f6(x9, x10) :|: x9 > 50
7.80/2.78	f8(x11, x12) -> f7(x11, x12) :|: TRUE
7.80/2.78	f9(x13, x14) -> f7(x13, x14) :|: TRUE
7.80/2.78	f7(x26, x27) -> f10(x28, x27) :|: TRUE && x28 = x26 + 1
7.80/2.78	f3(x17, x18) -> f4(x17, x18) :|: x18 >= 0
7.80/2.78	f10(x19, x20) -> f3(x19, x20) :|: TRUE
7.80/2.78	f3(x21, x22) -> f11(x21, x22) :|: x22 < 0
7.80/2.78	Start term: f1(x, y)
7.80/2.78	
7.80/2.78	----------------------------------------
7.80/2.78	
7.80/2.78	(3) TerminationGraphProcessor (SOUND)
7.80/2.78	Constructed the termination graph and obtained one non-trivial SCC.
7.80/2.78	
7.80/2.78	----------------------------------------
7.80/2.78	
7.80/2.78	(4)
7.80/2.78	Obligation:
7.80/2.78	Rules:
7.80/2.78	f3(x17, x18) -> f4(x17, x18) :|: x18 >= 0
7.80/2.78	f10(x19, x20) -> f3(x19, x20) :|: TRUE
7.80/2.78	f7(x26, x27) -> f10(x28, x27) :|: TRUE && x28 = x26 + 1
7.80/2.78	f8(x11, x12) -> f7(x11, x12) :|: TRUE
7.80/2.78	f5(x3, x4) -> f8(x3, arith) :|: TRUE && arith = x4 + 1
7.80/2.78	f4(x7, x8) -> f5(x7, x8) :|: x7 <= 50
7.80/2.78	f9(x13, x14) -> f7(x13, x14) :|: TRUE
7.80/2.78	f6(x23, x24) -> f9(x23, x25) :|: TRUE && x25 = x24 - 1
7.80/2.78	f4(x9, x10) -> f6(x9, x10) :|: x9 > 50
7.80/2.78	
7.80/2.78	----------------------------------------
7.80/2.78	
7.80/2.78	(5) IntTRSCompressionProof (EQUIVALENT)
7.80/2.78	Compressed rules.
7.80/2.78	----------------------------------------
7.80/2.78	
7.80/2.78	(6)
7.80/2.78	Obligation:
7.80/2.78	Rules:
7.80/2.78	f7(x26:0, x27:0) -> f7(x26:0 + 1, x27:0 - 1) :|: x27:0 > -1 && x26:0 > 49
7.80/2.78	f7(x, x1) -> f7(x + 1, x1 + 1) :|: x1 > -1 && x < 50
7.80/2.78	
7.80/2.78	----------------------------------------
7.80/2.78	
7.80/2.78	(7) PolynomialOrderProcessor (EQUIVALENT)
7.80/2.78	Found the following polynomial interpretation:
7.80/2.78	[f7(x, x1)] = 49 - x + x1
7.80/2.78	
7.80/2.78	The following rules are decreasing:
7.80/2.78	f7(x26:0, x27:0) -> f7(x26:0 + 1, x27:0 - 1) :|: x27:0 > -1 && x26:0 > 49
7.80/2.78	The following rules are bounded:
7.80/2.78	f7(x, x1) -> f7(x + 1, x1 + 1) :|: x1 > -1 && x < 50
7.80/2.78	
7.80/2.78	----------------------------------------
7.80/2.78	
7.80/2.78	(8)
7.80/2.78	Complex Obligation (AND)
7.80/2.78	
7.80/2.78	----------------------------------------
7.80/2.78	
7.80/2.78	(9)
7.80/2.78	Obligation:
7.80/2.78	Rules:
7.80/2.78	f7(x, x1) -> f7(x + 1, x1 + 1) :|: x1 > -1 && x < 50
7.80/2.78	
7.80/2.78	----------------------------------------
7.80/2.78	
7.80/2.78	(10) PolynomialOrderProcessor (EQUIVALENT)
7.80/2.78	Found the following polynomial interpretation:
7.80/2.78	[f7(x, x1)] = 49 - x
7.80/2.78	
7.80/2.78	The following rules are decreasing:
7.80/2.78	f7(x, x1) -> f7(x + 1, x1 + 1) :|: x1 > -1 && x < 50
7.80/2.78	The following rules are bounded:
7.80/2.78	f7(x, x1) -> f7(x + 1, x1 + 1) :|: x1 > -1 && x < 50
7.80/2.78	
7.80/2.78	----------------------------------------
7.80/2.78	
7.80/2.78	(11)
7.80/2.78	YES
7.80/2.78	
7.80/2.78	----------------------------------------
7.80/2.78	
7.80/2.78	(12)
7.80/2.78	Obligation:
7.80/2.78	Rules:
7.80/2.78	f7(x26:0, x27:0) -> f7(x26:0 + 1, x27:0 - 1) :|: x27:0 > -1 && x26:0 > 49
7.80/2.78	
7.80/2.78	----------------------------------------
7.80/2.78	
7.80/2.78	(13) PolynomialOrderProcessor (EQUIVALENT)
7.80/2.78	Found the following polynomial interpretation:
7.80/2.78	[f7(x, x1)] = x1
7.80/2.78	
7.80/2.78	The following rules are decreasing:
7.80/2.78	f7(x26:0, x27:0) -> f7(x26:0 + 1, x27:0 - 1) :|: x27:0 > -1 && x26:0 > 49
7.80/2.78	The following rules are bounded:
7.80/2.78	f7(x26:0, x27:0) -> f7(x26:0 + 1, x27:0 - 1) :|: x27:0 > -1 && x26:0 > 49
7.80/2.78	
7.80/2.78	----------------------------------------
7.80/2.78	
7.80/2.78	(14)
7.80/2.78	YES
8.05/2.84	EOF