6.38/2.43	YES
6.52/2.44	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
6.52/2.44	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.52/2.44	
6.52/2.44	
6.52/2.44	Termination of the given C Problem could be proven:
6.52/2.44	
6.52/2.44	(0) C Problem
6.52/2.44	(1) CToIRSProof [EQUIVALENT, 0 ms]
6.52/2.44	(2) IntTRS
6.52/2.44	(3) TerminationGraphProcessor [SOUND, 66 ms]
6.52/2.44	(4) IntTRS
6.52/2.44	(5) IntTRSCompressionProof [EQUIVALENT, 16 ms]
6.52/2.44	(6) IntTRS
6.52/2.44	(7) RankingReductionPairProof [EQUIVALENT, 8 ms]
6.52/2.44	(8) IntTRS
6.52/2.44	(9) PolynomialOrderProcessor [EQUIVALENT, 2 ms]
6.52/2.44	(10) YES
6.52/2.44	
6.52/2.44	
6.52/2.44	----------------------------------------
6.52/2.44	
6.52/2.44	(0)
6.52/2.44	Obligation:
6.52/2.44	c file /export/starexec/sandbox/benchmark/theBenchmark.c
6.52/2.44	----------------------------------------
6.52/2.44	
6.52/2.44	(1) CToIRSProof (EQUIVALENT)
6.52/2.44	Parsed C Integer Program as IRS.
6.52/2.44	----------------------------------------
6.52/2.44	
6.52/2.44	(2)
6.52/2.44	Obligation:
6.52/2.44	Rules:
6.52/2.44	f1(x, y) -> f2(x_1, y) :|: TRUE
6.52/2.44	f2(x1, x2) -> f3(x1, x3) :|: TRUE
6.52/2.44	f5(x4, x5) -> f8(arith, x5) :|: TRUE && arith = x4 - 1
6.52/2.44	f8(x6, x7) -> f9(x6, x8) :|: TRUE
6.52/2.44	f6(x27, x28) -> f10(x27, x29) :|: TRUE && x29 = x28 - 1
6.52/2.44	f4(x11, x12) -> f5(x11, x12) :|: x13 < 0
6.52/2.44	f4(x30, x31) -> f5(x30, x31) :|: x32 > 0
6.52/2.44	f4(x14, x15) -> f6(x14, x15) :|: x16 = 0
6.52/2.44	f9(x17, x18) -> f7(x17, x18) :|: TRUE
6.52/2.44	f10(x19, x20) -> f7(x19, x20) :|: TRUE
6.52/2.44	f3(x21, x22) -> f4(x21, x22) :|: x21 > 0 && x22 > 0
6.52/2.44	f7(x23, x24) -> f3(x23, x24) :|: TRUE
6.52/2.44	f3(x25, x26) -> f11(x25, x26) :|: x25 <= 0
6.52/2.44	f3(x33, x34) -> f11(x33, x34) :|: x34 <= 0
6.52/2.44	Start term: f1(x, y)
6.52/2.44	
6.52/2.44	----------------------------------------
6.52/2.44	
6.52/2.44	(3) TerminationGraphProcessor (SOUND)
6.52/2.44	Constructed the termination graph and obtained one non-trivial SCC.
6.52/2.44	
6.52/2.44	----------------------------------------
6.52/2.44	
6.52/2.44	(4)
6.52/2.44	Obligation:
6.52/2.44	Rules:
6.52/2.44	f3(x21, x22) -> f4(x21, x22) :|: x21 > 0 && x22 > 0
6.52/2.44	f7(x23, x24) -> f3(x23, x24) :|: TRUE
6.52/2.44	f9(x17, x18) -> f7(x17, x18) :|: TRUE
6.52/2.44	f8(x6, x7) -> f9(x6, x8) :|: TRUE
6.52/2.44	f5(x4, x5) -> f8(arith, x5) :|: TRUE && arith = x4 - 1
6.52/2.44	f4(x11, x12) -> f5(x11, x12) :|: x13 < 0
6.52/2.44	f4(x30, x31) -> f5(x30, x31) :|: x32 > 0
6.52/2.44	f10(x19, x20) -> f7(x19, x20) :|: TRUE
6.52/2.44	f6(x27, x28) -> f10(x27, x29) :|: TRUE && x29 = x28 - 1
6.52/2.44	f4(x14, x15) -> f6(x14, x15) :|: x16 = 0
6.52/2.44	
6.52/2.44	----------------------------------------
6.52/2.44	
6.52/2.44	(5) IntTRSCompressionProof (EQUIVALENT)
6.52/2.44	Compressed rules.
6.52/2.44	----------------------------------------
6.52/2.44	
6.52/2.44	(6)
6.52/2.44	Obligation:
6.52/2.44	Rules:
6.52/2.44	f7(x23:0, x24:0) -> f7(x23:0, x24:0 - 1) :|: x23:0 > 0 && x24:0 > 0
6.52/2.44	f7(x, x1) -> f7(x - 1, x2) :|: x > 0 && x1 > 0 && x3 < 0
6.52/2.44	f7(x4, x5) -> f7(x4 - 1, x6) :|: x4 > 0 && x5 > 0 && x7 > 0
6.52/2.44	
6.52/2.44	----------------------------------------
6.52/2.44	
6.52/2.44	(7) RankingReductionPairProof (EQUIVALENT)
6.52/2.44	Interpretation:
6.52/2.44	[ f7 ] = f7_1
6.52/2.44	
6.52/2.44	The following rules are decreasing:
6.52/2.44	f7(x, x1) -> f7(x - 1, x2) :|: x > 0 && x1 > 0 && x3 < 0
6.52/2.44	f7(x4, x5) -> f7(x4 - 1, x6) :|: x4 > 0 && x5 > 0 && x7 > 0
6.52/2.44	
6.52/2.44	The following rules are bounded:
6.52/2.44	f7(x23:0, x24:0) -> f7(x23:0, x24:0 - 1) :|: x23:0 > 0 && x24:0 > 0
6.52/2.44	f7(x, x1) -> f7(x - 1, x2) :|: x > 0 && x1 > 0 && x3 < 0
6.52/2.44	f7(x4, x5) -> f7(x4 - 1, x6) :|: x4 > 0 && x5 > 0 && x7 > 0
6.52/2.44	
6.52/2.44	
6.52/2.44	----------------------------------------
6.52/2.44	
6.52/2.44	(8)
6.52/2.44	Obligation:
6.52/2.44	Rules:
6.52/2.44	f7(x23:0, x24:0) -> f7(x23:0, x24:0 - 1) :|: x23:0 > 0 && x24:0 > 0
6.52/2.44	
6.52/2.44	----------------------------------------
6.52/2.44	
6.52/2.44	(9) PolynomialOrderProcessor (EQUIVALENT)
6.52/2.44	Found the following polynomial interpretation:
6.52/2.44	[f7(x, x1)] = x1
6.52/2.44	
6.52/2.44	The following rules are decreasing:
6.52/2.44	f7(x23:0, x24:0) -> f7(x23:0, x24:0 - 1) :|: x23:0 > 0 && x24:0 > 0
6.52/2.44	The following rules are bounded:
6.52/2.44	f7(x23:0, x24:0) -> f7(x23:0, x24:0 - 1) :|: x23:0 > 0 && x24:0 > 0
6.52/2.44	
6.52/2.44	----------------------------------------
6.52/2.44	
6.52/2.44	(10)
6.52/2.44	YES
6.52/2.47	EOF