4.95/2.07	YES
4.95/2.09	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.95/2.09	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.95/2.09	
4.95/2.09	
4.95/2.09	Termination of the given C Problem could be proven:
4.95/2.09	
4.95/2.09	(0) C Problem
4.95/2.09	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.95/2.09	(2) IntTRS
4.95/2.09	(3) TerminationGraphProcessor [SOUND, 49 ms]
4.95/2.09	(4) IntTRS
4.95/2.09	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
4.95/2.09	(6) IntTRS
4.95/2.09	(7) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
4.95/2.09	(8) IntTRS
4.95/2.09	(9) RankingReductionPairProof [EQUIVALENT, 13 ms]
4.95/2.09	(10) YES
4.95/2.09	
4.95/2.09	
4.95/2.09	----------------------------------------
4.95/2.09	
4.95/2.09	(0)
4.95/2.09	Obligation:
4.95/2.09	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.95/2.09	----------------------------------------
4.95/2.09	
4.95/2.09	(1) CToIRSProof (EQUIVALENT)
4.95/2.09	Parsed C Integer Program as IRS.
4.95/2.09	----------------------------------------
4.95/2.09	
4.95/2.09	(2)
4.95/2.09	Obligation:
4.95/2.09	Rules:
4.95/2.09	f1(q, y) -> f2(x_1, y) :|: TRUE
4.95/2.09	f2(x, x1) -> f3(x, x2) :|: TRUE
4.95/2.09	f5(x3, x4) -> f8(x3, 0) :|: TRUE
4.95/2.09	f8(x5, x6) -> f9(x7, x6) :|: TRUE
4.95/2.09	f6(x8, x9) -> f10(x8, arith) :|: TRUE && arith = x9 - 1
4.95/2.09	f10(x26, x27) -> f11(x28, x27) :|: TRUE && x28 = x26 - 1
4.95/2.09	f4(x12, x13) -> f5(x12, x13) :|: x13 > 0
4.95/2.09	f4(x14, x15) -> f6(x14, x15) :|: x15 <= 0
4.95/2.09	f9(x16, x17) -> f7(x16, x17) :|: TRUE
4.95/2.09	f11(x18, x19) -> f7(x18, x19) :|: TRUE
4.95/2.09	f3(x20, x21) -> f4(x20, x21) :|: x20 > 0
4.95/2.09	f7(x22, x23) -> f3(x22, x23) :|: TRUE
4.95/2.09	f3(x24, x25) -> f12(x24, x25) :|: x24 <= 0
4.95/2.09	Start term: f1(q, y)
4.95/2.09	
4.95/2.09	----------------------------------------
4.95/2.09	
4.95/2.09	(3) TerminationGraphProcessor (SOUND)
4.95/2.09	Constructed the termination graph and obtained one non-trivial SCC.
4.95/2.09	
4.95/2.09	----------------------------------------
4.95/2.09	
4.95/2.09	(4)
4.95/2.09	Obligation:
4.95/2.09	Rules:
4.95/2.09	f3(x20, x21) -> f4(x20, x21) :|: x20 > 0
4.95/2.09	f7(x22, x23) -> f3(x22, x23) :|: TRUE
4.95/2.09	f9(x16, x17) -> f7(x16, x17) :|: TRUE
4.95/2.09	f8(x5, x6) -> f9(x7, x6) :|: TRUE
4.95/2.09	f5(x3, x4) -> f8(x3, 0) :|: TRUE
4.95/2.09	f4(x12, x13) -> f5(x12, x13) :|: x13 > 0
4.95/2.09	f11(x18, x19) -> f7(x18, x19) :|: TRUE
4.95/2.09	f10(x26, x27) -> f11(x28, x27) :|: TRUE && x28 = x26 - 1
4.95/2.09	f6(x8, x9) -> f10(x8, arith) :|: TRUE && arith = x9 - 1
4.95/2.09	f4(x14, x15) -> f6(x14, x15) :|: x15 <= 0
4.95/2.09	
4.95/2.09	----------------------------------------
4.95/2.09	
4.95/2.09	(5) IntTRSCompressionProof (EQUIVALENT)
4.95/2.09	Compressed rules.
4.95/2.09	----------------------------------------
4.95/2.09	
4.95/2.09	(6)
4.95/2.09	Obligation:
4.95/2.09	Rules:
4.95/2.09	f7(x22:0, x23:0) -> f7(x22:0 - 1, x23:0 - 1) :|: x22:0 > 0 && x23:0 < 1
4.95/2.09	f7(x, x1) -> f7(x2, 0) :|: x > 0 && x1 > 0
4.95/2.09	
4.95/2.09	----------------------------------------
4.95/2.09	
4.95/2.09	(7) PolynomialOrderProcessor (EQUIVALENT)
4.95/2.09	Found the following polynomial interpretation:
4.95/2.09	[f7(x, x1)] = -1 + x1
4.95/2.09	
4.95/2.09	The following rules are decreasing:
4.95/2.09	f7(x22:0, x23:0) -> f7(x22:0 - 1, x23:0 - 1) :|: x22:0 > 0 && x23:0 < 1
4.95/2.09	f7(x, x1) -> f7(x2, 0) :|: x > 0 && x1 > 0
4.95/2.09	The following rules are bounded:
4.95/2.09	f7(x, x1) -> f7(x2, 0) :|: x > 0 && x1 > 0
4.95/2.09	
4.95/2.09	----------------------------------------
4.95/2.09	
4.95/2.09	(8)
4.95/2.09	Obligation:
4.95/2.09	Rules:
4.95/2.09	f7(x22:0, x23:0) -> f7(x22:0 - 1, x23:0 - 1) :|: x22:0 > 0 && x23:0 < 1
4.95/2.09	
4.95/2.09	----------------------------------------
4.95/2.09	
4.95/2.09	(9) RankingReductionPairProof (EQUIVALENT)
4.95/2.09	Interpretation:
4.95/2.09	[ f7 ] = f7_1
4.95/2.09	
4.95/2.09	The following rules are decreasing:
4.95/2.09	f7(x22:0, x23:0) -> f7(x22:0 - 1, x23:0 - 1) :|: x22:0 > 0 && x23:0 < 1
4.95/2.09	
4.95/2.09	The following rules are bounded:
4.95/2.09	f7(x22:0, x23:0) -> f7(x22:0 - 1, x23:0 - 1) :|: x22:0 > 0 && x23:0 < 1
4.95/2.09	
4.95/2.09	
4.95/2.09	----------------------------------------
4.95/2.09	
4.95/2.09	(10)
4.95/2.09	YES
5.32/2.12	EOF