6.36/2.40	YES
6.36/2.42	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
6.36/2.42	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.36/2.42	
6.36/2.42	
6.36/2.42	Termination of the given C Problem could be proven:
6.36/2.42	
6.36/2.42	(0) C Problem
6.36/2.42	(1) CToIRSProof [EQUIVALENT, 0 ms]
6.36/2.42	(2) IntTRS
6.36/2.42	(3) TerminationGraphProcessor [SOUND, 52 ms]
6.36/2.42	(4) IntTRS
6.36/2.42	(5) IntTRSCompressionProof [EQUIVALENT, 52 ms]
6.36/2.42	(6) IntTRS
6.36/2.42	(7) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
6.36/2.42	(8) IntTRS
6.36/2.42	(9) RankingReductionPairProof [EQUIVALENT, 0 ms]
6.36/2.42	(10) YES
6.36/2.42	
6.36/2.42	
6.36/2.42	----------------------------------------
6.36/2.42	
6.36/2.42	(0)
6.36/2.42	Obligation:
6.36/2.42	c file /export/starexec/sandbox/benchmark/theBenchmark.c
6.36/2.42	----------------------------------------
6.36/2.42	
6.36/2.42	(1) CToIRSProof (EQUIVALENT)
6.36/2.42	Parsed C Integer Program as IRS.
6.36/2.42	----------------------------------------
6.36/2.42	
6.36/2.42	(2)
6.36/2.42	Obligation:
6.36/2.42	Rules:
6.36/2.42	f2(x, y) -> f3(x, arith) :|: TRUE && arith = y - 1
6.36/2.42	f4(x20, x21) -> f7(x22, x21) :|: TRUE && x22 = x20 - 1
6.36/2.42	f7(x3, x4) -> f8(x3, x5) :|: TRUE
6.36/2.42	f3(x6, x7) -> f4(x6, x7) :|: x7 < 0
6.36/2.42	f3(x8, x9) -> f5(x8, x9) :|: x9 >= 0
6.36/2.42	f8(x10, x11) -> f6(x10, x11) :|: TRUE
6.36/2.42	f5(x12, x13) -> f6(x12, x13) :|: TRUE
6.36/2.42	f1(x14, x15) -> f2(x14, x15) :|: x14 >= 0 && x15 >= 0
6.36/2.42	f6(x16, x17) -> f1(x16, x17) :|: TRUE
6.36/2.42	f1(x18, x19) -> f9(x18, x19) :|: x18 < 0
6.36/2.42	f1(x23, x24) -> f9(x23, x24) :|: x24 < 0
6.36/2.42	Start term: f1(x, y)
6.36/2.42	
6.36/2.42	----------------------------------------
6.36/2.42	
6.36/2.42	(3) TerminationGraphProcessor (SOUND)
6.36/2.42	Constructed the termination graph and obtained one non-trivial SCC.
6.36/2.42	
6.36/2.42	----------------------------------------
6.36/2.42	
6.36/2.42	(4)
6.36/2.42	Obligation:
6.36/2.42	Rules:
6.36/2.42	f1(x14, x15) -> f2(x14, x15) :|: x14 >= 0 && x15 >= 0
6.36/2.42	f6(x16, x17) -> f1(x16, x17) :|: TRUE
6.36/2.42	f8(x10, x11) -> f6(x10, x11) :|: TRUE
6.36/2.42	f7(x3, x4) -> f8(x3, x5) :|: TRUE
6.36/2.42	f4(x20, x21) -> f7(x22, x21) :|: TRUE && x22 = x20 - 1
6.36/2.42	f3(x6, x7) -> f4(x6, x7) :|: x7 < 0
6.36/2.42	f2(x, y) -> f3(x, arith) :|: TRUE && arith = y - 1
6.36/2.42	f5(x12, x13) -> f6(x12, x13) :|: TRUE
6.36/2.42	f3(x8, x9) -> f5(x8, x9) :|: x9 >= 0
6.36/2.42	
6.36/2.42	----------------------------------------
6.36/2.42	
6.36/2.42	(5) IntTRSCompressionProof (EQUIVALENT)
6.36/2.42	Compressed rules.
6.36/2.42	----------------------------------------
6.36/2.42	
6.36/2.42	(6)
6.36/2.42	Obligation:
6.36/2.42	Rules:
6.36/2.42	f3(x8:0, x9:0) -> f3(x8:0, x9:0 - 1) :|: x9:0 > -1 && x8:0 > -1
6.36/2.42	f3(x6:0, x7:0) -> f3(x6:0 - 1, x5:0 - 1) :|: x6:0 > 0 && x5:0 > -1 && x7:0 < 0
6.36/2.42	
6.36/2.42	----------------------------------------
6.36/2.42	
6.36/2.42	(7) PolynomialOrderProcessor (EQUIVALENT)
6.36/2.42	Found the following polynomial interpretation:
6.36/2.42	[f3(x, x1)] = x
6.36/2.42	
6.36/2.42	The following rules are decreasing:
6.36/2.42	f3(x6:0, x7:0) -> f3(x6:0 - 1, x5:0 - 1) :|: x6:0 > 0 && x5:0 > -1 && x7:0 < 0
6.36/2.42	The following rules are bounded:
6.36/2.42	f3(x8:0, x9:0) -> f3(x8:0, x9:0 - 1) :|: x9:0 > -1 && x8:0 > -1
6.36/2.42	f3(x6:0, x7:0) -> f3(x6:0 - 1, x5:0 - 1) :|: x6:0 > 0 && x5:0 > -1 && x7:0 < 0
6.36/2.42	
6.36/2.42	----------------------------------------
6.36/2.42	
6.36/2.42	(8)
6.36/2.42	Obligation:
6.36/2.42	Rules:
6.36/2.42	f3(x8:0, x9:0) -> f3(x8:0, x9:0 - 1) :|: x9:0 > -1 && x8:0 > -1
6.36/2.42	
6.36/2.42	----------------------------------------
6.36/2.42	
6.36/2.42	(9) RankingReductionPairProof (EQUIVALENT)
6.36/2.42	Interpretation:
6.36/2.42	[ f3 ] = f3_2
6.36/2.42	
6.36/2.42	The following rules are decreasing:
6.36/2.42	f3(x8:0, x9:0) -> f3(x8:0, x9:0 - 1) :|: x9:0 > -1 && x8:0 > -1
6.36/2.42	
6.36/2.42	The following rules are bounded:
6.36/2.42	f3(x8:0, x9:0) -> f3(x8:0, x9:0 - 1) :|: x9:0 > -1 && x8:0 > -1
6.36/2.42	
6.36/2.42	
6.36/2.42	----------------------------------------
6.36/2.42	
6.36/2.42	(10)
6.36/2.42	YES
6.36/2.45	EOF