5.44/2.33	YES
5.44/2.35	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
5.44/2.35	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.44/2.35	
5.44/2.35	
5.44/2.35	Termination of the given C Problem could be proven:
5.44/2.35	
5.44/2.35	(0) C Problem
5.44/2.35	(1) CToIRSProof [EQUIVALENT, 0 ms]
5.44/2.35	(2) IntTRS
5.44/2.35	(3) TerminationGraphProcessor [SOUND, 62 ms]
5.44/2.35	(4) IntTRS
5.44/2.35	(5) IntTRSCompressionProof [EQUIVALENT, 34 ms]
5.44/2.35	(6) IntTRS
5.44/2.35	(7) RankingReductionPairProof [EQUIVALENT, 31 ms]
5.44/2.35	(8) IntTRS
5.44/2.35	(9) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
5.44/2.35	(10) IntTRS
5.44/2.35	(11) PolynomialOrderProcessor [EQUIVALENT, 3 ms]
5.44/2.35	(12) YES
5.44/2.35	
5.44/2.35	
5.44/2.35	----------------------------------------
5.44/2.35	
5.44/2.35	(0)
5.44/2.35	Obligation:
5.44/2.35	c file /export/starexec/sandbox/benchmark/theBenchmark.c
5.44/2.35	----------------------------------------
5.44/2.35	
5.44/2.35	(1) CToIRSProof (EQUIVALENT)
5.44/2.35	Parsed C Integer Program as IRS.
5.44/2.35	----------------------------------------
5.44/2.35	
5.44/2.35	(2)
5.44/2.35	Obligation:
5.44/2.35	Rules:
5.44/2.35	f1(i, j, N) -> f2(i, x_1, N) :|: TRUE
5.44/2.35	f2(x, x1, x2) -> f3(x, x1, x3) :|: TRUE
5.44/2.35	f3(x4, x5, x6) -> f4(x6, x5, x6) :|: TRUE
5.44/2.35	f6(x7, x8, x9) -> f9(x7, arith, x9) :|: TRUE && arith = x8 - 1
5.44/2.35	f7(x10, x11, x12) -> f10(x10, x12, x12) :|: TRUE
5.44/2.35	f10(x37, x38, x39) -> f11(x40, x38, x39) :|: TRUE && x40 = x37 - 1
5.44/2.35	f5(x16, x17, x18) -> f6(x16, x17, x18) :|: x17 > 0
5.44/2.35	f5(x19, x20, x21) -> f7(x19, x20, x21) :|: x20 <= 0
5.44/2.35	f9(x22, x23, x24) -> f8(x22, x23, x24) :|: TRUE
5.44/2.35	f11(x25, x26, x27) -> f8(x25, x26, x27) :|: TRUE
5.44/2.35	f4(x28, x29, x30) -> f5(x28, x29, x30) :|: x28 > 0
5.44/2.35	f8(x31, x32, x33) -> f4(x31, x32, x33) :|: TRUE
5.44/2.35	f4(x34, x35, x36) -> f12(x34, x35, x36) :|: x34 <= 0
5.44/2.35	Start term: f1(i, j, N)
5.44/2.35	
5.44/2.35	----------------------------------------
5.44/2.35	
5.44/2.35	(3) TerminationGraphProcessor (SOUND)
5.44/2.35	Constructed the termination graph and obtained one non-trivial SCC.
5.44/2.35	
5.44/2.35	----------------------------------------
5.44/2.35	
5.44/2.35	(4)
5.44/2.35	Obligation:
5.44/2.35	Rules:
5.44/2.35	f4(x28, x29, x30) -> f5(x28, x29, x30) :|: x28 > 0
5.44/2.35	f8(x31, x32, x33) -> f4(x31, x32, x33) :|: TRUE
5.44/2.35	f9(x22, x23, x24) -> f8(x22, x23, x24) :|: TRUE
5.44/2.35	f6(x7, x8, x9) -> f9(x7, arith, x9) :|: TRUE && arith = x8 - 1
5.44/2.35	f5(x16, x17, x18) -> f6(x16, x17, x18) :|: x17 > 0
5.44/2.35	f11(x25, x26, x27) -> f8(x25, x26, x27) :|: TRUE
5.44/2.35	f10(x37, x38, x39) -> f11(x40, x38, x39) :|: TRUE && x40 = x37 - 1
5.44/2.35	f7(x10, x11, x12) -> f10(x10, x12, x12) :|: TRUE
5.44/2.35	f5(x19, x20, x21) -> f7(x19, x20, x21) :|: x20 <= 0
5.44/2.35	
5.44/2.35	----------------------------------------
5.44/2.35	
5.44/2.35	(5) IntTRSCompressionProof (EQUIVALENT)
5.44/2.35	Compressed rules.
5.44/2.35	----------------------------------------
5.44/2.35	
5.44/2.35	(6)
5.44/2.35	Obligation:
5.44/2.35	Rules:
5.44/2.35	f8(x31:0, x32:0, x33:0) -> f8(x31:0, x32:0 - 1, x33:0) :|: x31:0 > 0 && x32:0 > 0
5.44/2.35	f8(x, x1, x2) -> f8(x - 1, x2, x2) :|: x > 0 && x1 < 1
5.44/2.35	
5.44/2.35	----------------------------------------
5.44/2.35	
5.44/2.35	(7) RankingReductionPairProof (EQUIVALENT)
5.44/2.35	Interpretation:
5.44/2.35	[ f8 ] = f8_1
5.44/2.35	
5.44/2.35	The following rules are decreasing:
5.44/2.35	f8(x, x1, x2) -> f8(x - 1, x2, x2) :|: x > 0 && x1 < 1
5.44/2.35	
5.44/2.35	The following rules are bounded:
5.44/2.35	f8(x31:0, x32:0, x33:0) -> f8(x31:0, x32:0 - 1, x33:0) :|: x31:0 > 0 && x32:0 > 0
5.44/2.35	f8(x, x1, x2) -> f8(x - 1, x2, x2) :|: x > 0 && x1 < 1
5.44/2.35	
5.44/2.35	
5.44/2.35	----------------------------------------
5.44/2.35	
5.44/2.35	(8)
5.44/2.35	Obligation:
5.44/2.35	Rules:
5.44/2.35	f8(x31:0, x32:0, x33:0) -> f8(x31:0, x32:0 - 1, x33:0) :|: x31:0 > 0 && x32:0 > 0
5.44/2.35	
5.44/2.35	----------------------------------------
5.44/2.35	
5.44/2.35	(9) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
5.44/2.35	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
5.44/2.35	
5.44/2.35	   f8(x1, x2, x3) -> f8(x1, x2)
5.44/2.35	
5.44/2.35	----------------------------------------
5.44/2.35	
5.44/2.35	(10)
5.44/2.35	Obligation:
5.44/2.35	Rules:
5.44/2.35	f8(x31:0, x32:0) -> f8(x31:0, x32:0 - 1) :|: x31:0 > 0 && x32:0 > 0
5.44/2.35	
5.44/2.35	----------------------------------------
5.44/2.35	
5.44/2.35	(11) PolynomialOrderProcessor (EQUIVALENT)
5.44/2.35	Found the following polynomial interpretation:
5.44/2.35	[f8(x, x1)] = x1
5.44/2.35	
5.44/2.35	The following rules are decreasing:
5.44/2.35	f8(x31:0, x32:0) -> f8(x31:0, x32:0 - 1) :|: x31:0 > 0 && x32:0 > 0
5.44/2.35	The following rules are bounded:
5.44/2.35	f8(x31:0, x32:0) -> f8(x31:0, x32:0 - 1) :|: x31:0 > 0 && x32:0 > 0
5.44/2.35	
5.44/2.35	----------------------------------------
5.44/2.35	
5.44/2.35	(12)
5.44/2.35	YES
5.94/2.38	EOF