4.98/2.10	YES
5.20/2.11	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
5.20/2.11	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.20/2.11	
5.20/2.11	
5.20/2.11	Termination of the given C Problem could be proven:
5.20/2.11	
5.20/2.11	(0) C Problem
5.20/2.11	(1) CToIRSProof [EQUIVALENT, 0 ms]
5.20/2.11	(2) IntTRS
5.20/2.11	(3) TerminationGraphProcessor [SOUND, 58 ms]
5.20/2.11	(4) IntTRS
5.20/2.11	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
5.20/2.11	(6) IntTRS
5.20/2.11	(7) RankingReductionPairProof [EQUIVALENT, 21 ms]
5.20/2.11	(8) IntTRS
5.20/2.11	(9) PolynomialOrderProcessor [EQUIVALENT, 2 ms]
5.20/2.11	(10) YES
5.20/2.11	
5.20/2.11	
5.20/2.11	----------------------------------------
5.20/2.11	
5.20/2.11	(0)
5.20/2.11	Obligation:
5.20/2.11	c file /export/starexec/sandbox/benchmark/theBenchmark.c
5.20/2.11	----------------------------------------
5.20/2.11	
5.20/2.11	(1) CToIRSProof (EQUIVALENT)
5.20/2.11	Parsed C Integer Program as IRS.
5.20/2.11	----------------------------------------
5.20/2.11	
5.20/2.11	(2)
5.20/2.11	Obligation:
5.20/2.11	Rules:
5.20/2.11	f1(x, y) -> f2(x_1, y) :|: TRUE
5.20/2.11	f2(x1, x2) -> f3(x1, x3) :|: TRUE
5.20/2.11	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 + x5
5.20/2.11	f6(x22, x23) -> f9(x22, x24) :|: TRUE && x24 = x23 - 1
5.20/2.11	f5(x8, x9) -> f6(x8, x9) :|: x9 >= 0
5.20/2.11	f5(x10, x11) -> f7(x10, x11) :|: x11 < 0
5.20/2.11	f9(x12, x13) -> f8(x12, x13) :|: TRUE
5.20/2.11	f7(x14, x15) -> f8(x14, x15) :|: TRUE
5.20/2.11	f3(x16, x17) -> f4(x16, x17) :|: x16 >= 0
5.20/2.11	f8(x18, x19) -> f3(x18, x19) :|: TRUE
5.20/2.11	f3(x20, x21) -> f10(x20, x21) :|: x20 < 0
5.20/2.11	Start term: f1(x, y)
5.20/2.11	
5.20/2.11	----------------------------------------
5.20/2.11	
5.20/2.11	(3) TerminationGraphProcessor (SOUND)
5.20/2.11	Constructed the termination graph and obtained one non-trivial SCC.
5.20/2.11	
5.20/2.11	----------------------------------------
5.20/2.11	
5.20/2.11	(4)
5.20/2.11	Obligation:
5.20/2.11	Rules:
5.20/2.11	f3(x16, x17) -> f4(x16, x17) :|: x16 >= 0
5.20/2.11	f8(x18, x19) -> f3(x18, x19) :|: TRUE
5.20/2.11	f9(x12, x13) -> f8(x12, x13) :|: TRUE
5.20/2.11	f6(x22, x23) -> f9(x22, x24) :|: TRUE && x24 = x23 - 1
5.20/2.11	f5(x8, x9) -> f6(x8, x9) :|: x9 >= 0
5.20/2.11	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 + x5
5.20/2.11	f7(x14, x15) -> f8(x14, x15) :|: TRUE
5.20/2.11	f5(x10, x11) -> f7(x10, x11) :|: x11 < 0
5.20/2.11	
5.20/2.11	----------------------------------------
5.20/2.11	
5.20/2.11	(5) IntTRSCompressionProof (EQUIVALENT)
5.20/2.11	Compressed rules.
5.20/2.11	----------------------------------------
5.20/2.11	
5.20/2.11	(6)
5.20/2.11	Obligation:
5.20/2.11	Rules:
5.20/2.11	f5(x10:0, x11:0) -> f5(x10:0 + x11:0, x11:0) :|: x11:0 < 0 && x10:0 > -1
5.20/2.11	f5(x8:0, x9:0) -> f5(x8:0 + (x9:0 - 1), x9:0 - 1) :|: x9:0 > -1 && x8:0 > -1
5.20/2.11	
5.20/2.11	----------------------------------------
5.20/2.11	
5.20/2.11	(7) RankingReductionPairProof (EQUIVALENT)
5.20/2.11	Interpretation:
5.20/2.11	[ f5 ] = f5_2
5.20/2.11	
5.20/2.11	The following rules are decreasing:
5.20/2.11	f5(x8:0, x9:0) -> f5(x8:0 + (x9:0 - 1), x9:0 - 1) :|: x9:0 > -1 && x8:0 > -1
5.20/2.11	
5.20/2.11	The following rules are bounded:
5.20/2.11	f5(x8:0, x9:0) -> f5(x8:0 + (x9:0 - 1), x9:0 - 1) :|: x9:0 > -1 && x8:0 > -1
5.20/2.11	
5.20/2.11	
5.20/2.11	----------------------------------------
5.20/2.11	
5.20/2.11	(8)
5.20/2.11	Obligation:
5.20/2.11	Rules:
5.20/2.11	f5(x10:0, x11:0) -> f5(x10:0 + x11:0, x11:0) :|: x11:0 < 0 && x10:0 > -1
5.20/2.11	
5.20/2.11	----------------------------------------
5.20/2.11	
5.20/2.11	(9) PolynomialOrderProcessor (EQUIVALENT)
5.20/2.11	Found the following polynomial interpretation:
5.20/2.11	[f5(x, x1)] = x
5.20/2.11	
5.20/2.11	The following rules are decreasing:
5.20/2.11	f5(x10:0, x11:0) -> f5(x10:0 + x11:0, x11:0) :|: x11:0 < 0 && x10:0 > -1
5.20/2.11	The following rules are bounded:
5.20/2.11	f5(x10:0, x11:0) -> f5(x10:0 + x11:0, x11:0) :|: x11:0 < 0 && x10:0 > -1
5.20/2.11	
5.20/2.11	----------------------------------------
5.20/2.11	
5.20/2.11	(10)
5.20/2.11	YES
5.26/2.14	EOF