5.21/2.25	YES
5.21/2.26	proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
5.21/2.26	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.21/2.26	
5.21/2.26	
5.21/2.26	Termination of the given C Problem could be proven:
5.21/2.26	
5.21/2.26	(0) C Problem
5.21/2.26	(1) CToIRSProof [EQUIVALENT, 0 ms]
5.21/2.26	(2) IntTRS
5.21/2.26	(3) TerminationGraphProcessor [SOUND, 53 ms]
5.21/2.26	(4) IntTRS
5.21/2.26	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
5.21/2.26	(6) IntTRS
5.21/2.26	(7) PolynomialOrderProcessor [EQUIVALENT, 19 ms]
5.21/2.26	(8) IntTRS
5.21/2.26	(9) RankingReductionPairProof [EQUIVALENT, 4 ms]
5.21/2.26	(10) YES
5.21/2.26	
5.21/2.26	
5.21/2.26	----------------------------------------
5.21/2.26	
5.21/2.26	(0)
5.21/2.26	Obligation:
5.21/2.26	c file /export/starexec/sandbox2/benchmark/theBenchmark.c
5.21/2.26	----------------------------------------
5.21/2.26	
5.21/2.26	(1) CToIRSProof (EQUIVALENT)
5.21/2.26	Parsed C Integer Program as IRS.
5.21/2.26	----------------------------------------
5.21/2.26	
5.21/2.26	(2)
5.21/2.26	Obligation:
5.21/2.26	Rules:
5.21/2.26	f1(x, y) -> f2(x_1, y) :|: TRUE
5.21/2.26	f3(x1, x2) -> f4(arith, x2) :|: TRUE && arith = x1 + 1
5.21/2.26	f4(x3, x4) -> f5(x3, 1) :|: TRUE
5.21/2.26	f6(x21, x22) -> f7(x21, x23) :|: TRUE && x23 = x22 + 1
5.21/2.26	f5(x7, x8) -> f6(x7, x8) :|: x7 >= x8
5.21/2.26	f7(x9, x10) -> f5(x9, x10) :|: TRUE
5.21/2.26	f5(x11, x12) -> f8(x11, x12) :|: x11 < x12
5.21/2.26	f8(x24, x25) -> f9(x26, x25) :|: TRUE && x26 = x24 - 2
5.21/2.26	f2(x15, x16) -> f3(x15, x16) :|: x15 >= 0
5.21/2.26	f9(x17, x18) -> f2(x17, x18) :|: TRUE
5.21/2.26	f2(x19, x20) -> f10(x19, x20) :|: x19 < 0
5.21/2.26	Start term: f1(x, y)
5.21/2.26	
5.21/2.26	----------------------------------------
5.21/2.26	
5.21/2.26	(3) TerminationGraphProcessor (SOUND)
5.21/2.26	Constructed the termination graph and obtained one non-trivial SCC.
5.21/2.26	
5.21/2.26	----------------------------------------
5.21/2.26	
5.21/2.26	(4)
5.21/2.26	Obligation:
5.21/2.26	Rules:
5.21/2.26	f2(x15, x16) -> f3(x15, x16) :|: x15 >= 0
5.21/2.26	f9(x17, x18) -> f2(x17, x18) :|: TRUE
5.21/2.26	f8(x24, x25) -> f9(x26, x25) :|: TRUE && x26 = x24 - 2
5.21/2.26	f5(x11, x12) -> f8(x11, x12) :|: x11 < x12
5.21/2.26	f4(x3, x4) -> f5(x3, 1) :|: TRUE
5.21/2.26	f3(x1, x2) -> f4(arith, x2) :|: TRUE && arith = x1 + 1
5.21/2.26	f7(x9, x10) -> f5(x9, x10) :|: TRUE
5.21/2.26	f6(x21, x22) -> f7(x21, x23) :|: TRUE && x23 = x22 + 1
5.21/2.26	f5(x7, x8) -> f6(x7, x8) :|: x7 >= x8
5.21/2.26	
5.21/2.26	----------------------------------------
5.21/2.26	
5.21/2.26	(5) IntTRSCompressionProof (EQUIVALENT)
5.21/2.26	Compressed rules.
5.21/2.26	----------------------------------------
5.21/2.26	
5.21/2.26	(6)
5.21/2.26	Obligation:
5.21/2.26	Rules:
5.21/2.26	f5(x7:0, x8:0) -> f5(x7:0, x8:0 + 1) :|: x8:0 <= x7:0
5.21/2.26	f5(x11:0, x12:0) -> f5(x11:0 - 1, 1) :|: x12:0 > x11:0 && x11:0 > 1
5.21/2.26	
5.21/2.26	----------------------------------------
5.21/2.26	
5.21/2.26	(7) PolynomialOrderProcessor (EQUIVALENT)
5.21/2.26	Found the following polynomial interpretation:
5.21/2.26	[f5(x, x1)] = x^2
5.21/2.26	
5.21/2.26	The following rules are decreasing:
5.21/2.26	f5(x11:0, x12:0) -> f5(x11:0 - 1, 1) :|: x12:0 > x11:0 && x11:0 > 1
5.21/2.26	The following rules are bounded:
5.21/2.26	f5(x7:0, x8:0) -> f5(x7:0, x8:0 + 1) :|: x8:0 <= x7:0
5.21/2.26	f5(x11:0, x12:0) -> f5(x11:0 - 1, 1) :|: x12:0 > x11:0 && x11:0 > 1
5.21/2.26	
5.21/2.26	----------------------------------------
5.21/2.26	
5.21/2.26	(8)
5.21/2.26	Obligation:
5.21/2.26	Rules:
5.21/2.26	f5(x7:0, x8:0) -> f5(x7:0, x8:0 + 1) :|: x8:0 <= x7:0
5.21/2.26	
5.21/2.26	----------------------------------------
5.21/2.26	
5.21/2.26	(9) RankingReductionPairProof (EQUIVALENT)
5.21/2.26	Interpretation:
5.21/2.26	[ f5 ] = -1*f5_2 + f5_1
5.21/2.26	
5.21/2.26	The following rules are decreasing:
5.21/2.26	f5(x7:0, x8:0) -> f5(x7:0, x8:0 + 1) :|: x8:0 <= x7:0
5.21/2.26	
5.21/2.26	The following rules are bounded:
5.21/2.26	f5(x7:0, x8:0) -> f5(x7:0, x8:0 + 1) :|: x8:0 <= x7:0
5.21/2.26	
5.21/2.26	
5.21/2.26	----------------------------------------
5.21/2.26	
5.21/2.26	(10)
5.21/2.26	YES
5.21/2.29	EOF