4.95/2.14	YES
4.95/2.16	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.95/2.16	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.95/2.16	
4.95/2.16	
4.95/2.16	Termination of the given C Problem could be proven:
4.95/2.16	
4.95/2.16	(0) C Problem
4.95/2.16	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.95/2.16	(2) IntTRS
4.95/2.16	(3) TerminationGraphProcessor [SOUND, 49 ms]
4.95/2.16	(4) IntTRS
4.95/2.16	(5) IntTRSCompressionProof [EQUIVALENT, 41 ms]
4.95/2.16	(6) IntTRS
4.95/2.16	(7) RankingReductionPairProof [EQUIVALENT, 29 ms]
4.95/2.16	(8) YES
4.95/2.16	
4.95/2.16	
4.95/2.16	----------------------------------------
4.95/2.16	
4.95/2.16	(0)
4.95/2.16	Obligation:
4.95/2.16	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.95/2.16	----------------------------------------
4.95/2.16	
4.95/2.16	(1) CToIRSProof (EQUIVALENT)
4.95/2.16	Parsed C Integer Program as IRS.
4.95/2.16	----------------------------------------
4.95/2.16	
4.95/2.16	(2)
4.95/2.16	Obligation:
4.95/2.16	Rules:
4.95/2.16	f1(x, y) -> f2(x_1, y) :|: TRUE
4.95/2.16	f2(x1, x2) -> f3(x1, x3) :|: TRUE
4.95/2.16	f5(x4, x5) -> f6(arith, x5) :|: TRUE && arith = x4 - 1
4.95/2.16	f6(x20, x21) -> f7(x20, x22) :|: TRUE && x22 = x21 - 1
4.95/2.16	f4(x8, x9) -> f5(x8, x9) :|: x9 > 0
4.95/2.16	f7(x10, x11) -> f4(x10, x11) :|: TRUE
4.95/2.16	f4(x12, x13) -> f8(x12, x13) :|: x13 <= 0
4.95/2.16	f3(x14, x15) -> f4(x14, x15) :|: x14 = x15 && x14 > 0
4.95/2.16	f8(x16, x17) -> f3(x16, x17) :|: TRUE
4.95/2.16	f3(x18, x19) -> f9(x18, x19) :|: x18 <= 0
4.95/2.16	f3(x23, x24) -> f9(x23, x24) :|: x23 < x24
4.95/2.16	f3(x25, x26) -> f9(x25, x26) :|: x25 > x26
4.95/2.16	Start term: f1(x, y)
4.95/2.16	
4.95/2.16	----------------------------------------
4.95/2.16	
4.95/2.16	(3) TerminationGraphProcessor (SOUND)
4.95/2.16	Constructed the termination graph and obtained one non-trivial SCC.
4.95/2.16	
4.95/2.16	----------------------------------------
4.95/2.16	
4.95/2.16	(4)
4.95/2.16	Obligation:
4.95/2.16	Rules:
4.95/2.16	f3(x14, x15) -> f4(x14, x15) :|: x14 = x15 && x14 > 0
4.95/2.16	f8(x16, x17) -> f3(x16, x17) :|: TRUE
4.95/2.16	f4(x12, x13) -> f8(x12, x13) :|: x13 <= 0
4.95/2.16	f7(x10, x11) -> f4(x10, x11) :|: TRUE
4.95/2.16	f6(x20, x21) -> f7(x20, x22) :|: TRUE && x22 = x21 - 1
4.95/2.16	f5(x4, x5) -> f6(arith, x5) :|: TRUE && arith = x4 - 1
4.95/2.16	f4(x8, x9) -> f5(x8, x9) :|: x9 > 0
4.95/2.16	
4.95/2.16	----------------------------------------
4.95/2.16	
4.95/2.16	(5) IntTRSCompressionProof (EQUIVALENT)
4.95/2.16	Compressed rules.
4.95/2.16	----------------------------------------
4.95/2.16	
4.95/2.16	(6)
4.95/2.16	Obligation:
4.95/2.16	Rules:
4.95/2.16	f4(x8:0, x9:0) -> f4(x8:0 - 1, x9:0 - 1) :|: x9:0 > 0
4.95/2.16	f4(x12:0, x12:01) -> f4(x12:0, x12:0) :|: x12:0 < 1 && x12:0 > 0 && x12:0 = x12:01
4.95/2.16	
4.95/2.16	----------------------------------------
4.95/2.16	
4.95/2.16	(7) RankingReductionPairProof (EQUIVALENT)
4.95/2.16	Interpretation:
4.95/2.16	[ f4 ] = f4_2
4.95/2.16	
4.95/2.16	The following rules are decreasing:
4.95/2.16	f4(x8:0, x9:0) -> f4(x8:0 - 1, x9:0 - 1) :|: x9:0 > 0
4.95/2.16	f4(x12:0, x12:01) -> f4(x12:0, x12:0) :|: x12:0 < 1 && x12:0 > 0 && x12:0 = x12:01
4.95/2.16	
4.95/2.16	The following rules are bounded:
4.95/2.16	f4(x8:0, x9:0) -> f4(x8:0 - 1, x9:0 - 1) :|: x9:0 > 0
4.95/2.16	f4(x12:0, x12:01) -> f4(x12:0, x12:0) :|: x12:0 < 1 && x12:0 > 0 && x12:0 = x12:01
4.95/2.16	
4.95/2.16	
4.95/2.16	----------------------------------------
4.95/2.16	
4.95/2.16	(8)
4.95/2.16	YES
4.95/2.19	EOF