8.18/2.97	YES
8.57/2.98	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
8.57/2.98	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
8.57/2.98	
8.57/2.98	
8.57/2.98	Termination of the given C Problem could be proven:
8.57/2.98	
8.57/2.98	(0) C Problem
8.57/2.98	(1) CToIRSProof [EQUIVALENT, 0 ms]
8.57/2.98	(2) IntTRS
8.57/2.98	(3) TerminationGraphProcessor [SOUND, 66 ms]
8.57/2.98	(4) IntTRS
8.57/2.98	(5) IntTRSCompressionProof [EQUIVALENT, 7 ms]
8.57/2.98	(6) IntTRS
8.57/2.98	(7) PolynomialOrderProcessor [EQUIVALENT, 2 ms]
8.57/2.98	(8) IntTRS
8.57/2.98	(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
8.57/2.98	(10) AND
8.57/2.98	    (11) IntTRS
8.57/2.98	        (12) TerminationGraphProcessor [EQUIVALENT, 3 ms]
8.57/2.98	        (13) YES
8.57/2.98	    (14) IntTRS
8.57/2.98	        (15) RankingReductionPairProof [EQUIVALENT, 4 ms]
8.57/2.98	        (16) YES
8.57/2.98	
8.57/2.98	
8.57/2.98	----------------------------------------
8.57/2.98	
8.57/2.98	(0)
8.57/2.98	Obligation:
8.57/2.98	c file /export/starexec/sandbox/benchmark/theBenchmark.c
8.57/2.98	----------------------------------------
8.57/2.98	
8.57/2.98	(1) CToIRSProof (EQUIVALENT)
8.57/2.98	Parsed C Integer Program as IRS.
8.57/2.98	----------------------------------------
8.57/2.98	
8.57/2.98	(2)
8.57/2.98	Obligation:
8.57/2.98	Rules:
8.57/2.98	f1(i, j) -> f2(x_1, j) :|: TRUE
8.57/2.98	f2(x, x1) -> f3(x, x2) :|: TRUE
8.57/2.98	f4(x3, x4) -> f5(x3, 0) :|: TRUE
8.57/2.98	f6(x5, x6) -> f7(x5, arith) :|: TRUE && arith = x6 + 1
8.57/2.98	f5(x7, x8) -> f6(x7, x8) :|: x7 > 2 && x8 <= 9
8.57/2.98	f7(x9, x10) -> f5(x9, x10) :|: TRUE
8.57/2.98	f5(x11, x12) -> f8(x11, x12) :|: x11 <= 2
8.57/2.98	f5(x21, x22) -> f8(x21, x22) :|: x22 > 9
8.57/2.98	f8(x23, x24) -> f9(x25, x24) :|: TRUE && x25 = x23 + 1
8.57/2.98	f3(x15, x16) -> f4(x15, x16) :|: x15 < 5
8.57/2.98	f9(x17, x18) -> f3(x17, x18) :|: TRUE
8.57/2.98	f3(x19, x20) -> f10(x19, x20) :|: x19 >= 5
8.57/2.98	Start term: f1(i, j)
8.57/2.98	
8.57/2.98	----------------------------------------
8.57/2.98	
8.57/2.98	(3) TerminationGraphProcessor (SOUND)
8.57/2.98	Constructed the termination graph and obtained one non-trivial SCC.
8.57/2.98	
8.57/2.98	----------------------------------------
8.57/2.98	
8.57/2.98	(4)
8.57/2.98	Obligation:
8.57/2.98	Rules:
8.57/2.98	f3(x15, x16) -> f4(x15, x16) :|: x15 < 5
8.57/2.98	f9(x17, x18) -> f3(x17, x18) :|: TRUE
8.57/2.98	f8(x23, x24) -> f9(x25, x24) :|: TRUE && x25 = x23 + 1
8.57/2.98	f5(x11, x12) -> f8(x11, x12) :|: x11 <= 2
8.57/2.98	f4(x3, x4) -> f5(x3, 0) :|: TRUE
8.57/2.98	f7(x9, x10) -> f5(x9, x10) :|: TRUE
8.57/2.98	f6(x5, x6) -> f7(x5, arith) :|: TRUE && arith = x6 + 1
8.57/2.98	f5(x7, x8) -> f6(x7, x8) :|: x7 > 2 && x8 <= 9
8.57/2.98	f5(x21, x22) -> f8(x21, x22) :|: x22 > 9
8.57/2.98	
8.57/2.98	----------------------------------------
8.57/2.98	
8.57/2.98	(5) IntTRSCompressionProof (EQUIVALENT)
8.57/2.98	Compressed rules.
8.57/2.98	----------------------------------------
8.57/2.98	
8.57/2.98	(6)
8.57/2.98	Obligation:
8.57/2.98	Rules:
8.57/2.98	f5(x7:0, x8:0) -> f5(x7:0, x8:0 + 1) :|: x7:0 > 2 && x8:0 < 10
8.57/2.98	f5(x11:0, x12:0) -> f5(x11:0 + 1, 0) :|: x11:0 < 3 && x11:0 < 4
8.57/2.98	f5(x21:0, x22:0) -> f5(x21:0 + 1, 0) :|: x22:0 > 9 && x21:0 < 4
8.57/2.98	
8.57/2.98	----------------------------------------
8.57/2.98	
8.57/2.98	(7) PolynomialOrderProcessor (EQUIVALENT)
8.57/2.98	Found the following polynomial interpretation:
8.57/2.98	[f5(x, x1)] = 11 - 7*x + x^2
8.57/2.98	
8.57/2.98	The following rules are decreasing:
8.57/2.98	f5(x11:0, x12:0) -> f5(x11:0 + 1, 0) :|: x11:0 < 3 && x11:0 < 4
8.57/2.98	The following rules are bounded:
8.57/2.98	f5(x11:0, x12:0) -> f5(x11:0 + 1, 0) :|: x11:0 < 3 && x11:0 < 4
8.57/2.98	
8.57/2.98	----------------------------------------
8.57/2.98	
8.57/2.98	(8)
8.57/2.98	Obligation:
8.57/2.98	Rules:
8.57/2.98	f5(x7:0, x8:0) -> f5(x7:0, x8:0 + 1) :|: x7:0 > 2 && x8:0 < 10
8.57/2.98	f5(x21:0, x22:0) -> f5(x21:0 + 1, 0) :|: x22:0 > 9 && x21:0 < 4
8.57/2.98	
8.57/2.98	----------------------------------------
8.57/2.98	
8.57/2.98	(9) PolynomialOrderProcessor (EQUIVALENT)
8.57/2.98	Found the following polynomial interpretation:
8.57/2.98	[f5(x, x1)] = 400 - 100*x - 20*x1 + x1^2
8.57/2.98	
8.57/2.98	The following rules are decreasing:
8.57/2.98	f5(x7:0, x8:0) -> f5(x7:0, x8:0 + 1) :|: x7:0 > 2 && x8:0 < 10
8.57/2.98	The following rules are bounded:
8.57/2.98	f5(x21:0, x22:0) -> f5(x21:0 + 1, 0) :|: x22:0 > 9 && x21:0 < 4
8.57/2.98	
8.57/2.98	----------------------------------------
8.57/2.98	
8.57/2.98	(10)
8.57/2.98	Complex Obligation (AND)
8.57/2.98	
8.57/2.98	----------------------------------------
8.57/2.98	
8.57/2.98	(11)
8.57/2.98	Obligation:
8.57/2.98	Rules:
8.57/2.98	f5(x21:0, x22:0) -> f5(x21:0 + 1, 0) :|: x22:0 > 9 && x21:0 < 4
8.57/2.98	
8.57/2.98	----------------------------------------
8.57/2.98	
8.57/2.98	(12) TerminationGraphProcessor (EQUIVALENT)
8.57/2.98	Constructed the termination graph and obtained no non-trivial SCC(s).
8.57/2.98	
8.57/2.98	----------------------------------------
8.57/2.98	
8.57/2.98	(13)
8.57/2.98	YES
8.57/2.98	
8.57/2.98	----------------------------------------
8.57/2.98	
8.57/2.98	(14)
8.57/2.98	Obligation:
8.57/2.98	Rules:
8.57/2.98	f5(x7:0, x8:0) -> f5(x7:0, x8:0 + 1) :|: x7:0 > 2 && x8:0 < 10
8.57/2.98	
8.57/2.98	----------------------------------------
8.57/2.98	
8.57/2.98	(15) RankingReductionPairProof (EQUIVALENT)
8.57/2.98	Interpretation:
8.57/2.98	[ f5 ] = -1*f5_2
8.57/2.98	
8.57/2.98	The following rules are decreasing:
8.57/2.98	f5(x7:0, x8:0) -> f5(x7:0, x8:0 + 1) :|: x7:0 > 2 && x8:0 < 10
8.57/2.98	
8.57/2.98	The following rules are bounded:
8.57/2.98	f5(x7:0, x8:0) -> f5(x7:0, x8:0 + 1) :|: x7:0 > 2 && x8:0 < 10
8.57/2.98	
8.57/2.98	
8.57/2.98	----------------------------------------
8.57/2.98	
8.57/2.98	(16)
8.57/2.98	YES
8.62/3.02	EOF