7.62/3.68	WORST_CASE(Omega(n^1), O(n^1))
7.62/3.69	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
7.62/3.69	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
7.62/3.69	
7.62/3.69	
7.62/3.69	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
7.62/3.69	
7.62/3.69	(0) CpxIntTrs
7.62/3.69	(1) Koat Proof [FINISHED, 114 ms]
7.62/3.69	(2) BOUNDS(1, n^1)
7.62/3.69	(3) Loat Proof [FINISHED, 2023 ms]
7.62/3.69	(4) BOUNDS(n^1, INF)
7.62/3.69	
7.62/3.69	
7.62/3.69	----------------------------------------
7.62/3.69	
7.62/3.69	(0)
7.62/3.69	Obligation:
7.62/3.69	Complexity Int TRS consisting of the following rules:
7.62/3.69	evalwcet1start(A, B, C, D) -> Com_1(evalwcet1entryin(A, B, C, D)) :|: TRUE
7.62/3.69	evalwcet1entryin(A, B, C, D) -> Com_1(evalwcet1bbin(A, 0, A, D)) :|: A >= 1
7.62/3.69	evalwcet1entryin(A, B, C, D) -> Com_1(evalwcet1returnin(A, B, C, D)) :|: 0 >= A
7.62/3.69	evalwcet1bbin(A, B, C, D) -> Com_1(evalwcet1bb1in(A, B, C, D)) :|: 0 >= E + 1
7.62/3.69	evalwcet1bbin(A, B, C, D) -> Com_1(evalwcet1bb1in(A, B, C, D)) :|: E >= 1
7.62/3.69	evalwcet1bbin(A, B, C, D) -> Com_1(evalwcet1bb4in(A, B, C, D)) :|: TRUE
7.62/3.69	evalwcet1bb1in(A, B, C, D) -> Com_1(evalwcet1bb6in(A, B, C, 0)) :|: B + 1 >= A
7.62/3.69	evalwcet1bb1in(A, B, C, D) -> Com_1(evalwcet1bb6in(A, B, C, B + 1)) :|: A >= B + 2
7.62/3.69	evalwcet1bb4in(A, B, C, D) -> Com_1(evalwcet1bb5in(A, B, C, D)) :|: 1 >= B
7.62/3.69	evalwcet1bb4in(A, B, C, D) -> Com_1(evalwcet1bb6in(A, B, C, B - 1)) :|: B >= 2
7.62/3.69	evalwcet1bb5in(A, B, C, D) -> Com_1(evalwcet1bb6in(A, B, C, 0)) :|: TRUE
7.62/3.69	evalwcet1bb6in(A, B, C, D) -> Com_1(evalwcet1bbin(A, D, C - 1, D)) :|: C >= 2
7.62/3.69	evalwcet1bb6in(A, B, C, D) -> Com_1(evalwcet1returnin(A, B, C, D)) :|: 1 >= C
7.62/3.69	evalwcet1returnin(A, B, C, D) -> Com_1(evalwcet1stop(A, B, C, D)) :|: TRUE
7.62/3.69	
7.62/3.69	The start-symbols are:[evalwcet1start_4]
7.62/3.69	
7.62/3.69	
7.62/3.69	----------------------------------------
7.62/3.69	
7.62/3.69	(1) Koat Proof (FINISHED)
7.62/3.69	YES(?, 11*ar_0 + 17)
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Initial complexity problem:
7.62/3.69	
7.62/3.69	1:	T:
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1entryin(ar_0, ar_1, ar_2, ar_3))
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, 0, ar_0, ar_3)) [ ar_0 >= 1 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3))
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0)) [ ar_1 + 1 >= ar_0 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 + 1)) [ ar_0 >= ar_1 + 2 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 - 1)) [ ar_1 >= 2 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0))
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, ar_3, ar_2 - 1, ar_3)) [ ar_2 >= 2 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_2 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1stop(ar_0, ar_1, ar_2, ar_3))
7.62/3.69	
7.62/3.69			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
7.62/3.69	
7.62/3.69		start location:	koat_start
7.62/3.69	
7.62/3.69		leaf cost:	0
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Repeatedly propagating knowledge in problem 1 produces the following problem:
7.62/3.69	
7.62/3.69	2:	T:
7.62/3.69	
7.62/3.69			(Comp: 1, Cost: 1)    evalwcet1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1entryin(ar_0, ar_1, ar_2, ar_3))
7.62/3.69	
7.62/3.69			(Comp: 1, Cost: 1)    evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, 0, ar_0, ar_3)) [ ar_0 >= 1 ]
7.62/3.69	
7.62/3.69			(Comp: 1, Cost: 1)    evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3))
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0)) [ ar_1 + 1 >= ar_0 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 + 1)) [ ar_0 >= ar_1 + 2 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 - 1)) [ ar_1 >= 2 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0))
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, ar_3, ar_2 - 1, ar_3)) [ ar_2 >= 2 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_2 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1stop(ar_0, ar_1, ar_2, ar_3))
7.62/3.69	
7.62/3.69			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
7.62/3.69	
7.62/3.69		start location:	koat_start
7.62/3.69	
7.62/3.69		leaf cost:	0
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	A polynomial rank function with
7.62/3.69	
7.62/3.69		Pol(evalwcet1start) = 2
7.62/3.69	
7.62/3.69		Pol(evalwcet1entryin) = 2
7.62/3.69	
7.62/3.69		Pol(evalwcet1bbin) = 2
7.62/3.69	
7.62/3.69		Pol(evalwcet1returnin) = 1
7.62/3.69	
7.62/3.69		Pol(evalwcet1bb1in) = 2
7.62/3.69	
7.62/3.69		Pol(evalwcet1bb4in) = 2
7.62/3.69	
7.62/3.69		Pol(evalwcet1bb6in) = 2
7.62/3.69	
7.62/3.69		Pol(evalwcet1bb5in) = 2
7.62/3.69	
7.62/3.69		Pol(evalwcet1stop) = 0
7.62/3.69	
7.62/3.69		Pol(koat_start) = 2
7.62/3.69	
7.62/3.69	orients all transitions weakly and the transitions
7.62/3.69	
7.62/3.69		evalwcet1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1stop(ar_0, ar_1, ar_2, ar_3))
7.62/3.69	
7.62/3.69		evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_2 ]
7.62/3.69	
7.62/3.69	strictly and produces the following problem:
7.62/3.69	
7.62/3.69	3:	T:
7.62/3.69	
7.62/3.69			(Comp: 1, Cost: 1)    evalwcet1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1entryin(ar_0, ar_1, ar_2, ar_3))
7.62/3.69	
7.62/3.69			(Comp: 1, Cost: 1)    evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, 0, ar_0, ar_3)) [ ar_0 >= 1 ]
7.62/3.69	
7.62/3.69			(Comp: 1, Cost: 1)    evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3))
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0)) [ ar_1 + 1 >= ar_0 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 + 1)) [ ar_0 >= ar_1 + 2 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 - 1)) [ ar_1 >= 2 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0))
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)    evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, ar_3, ar_2 - 1, ar_3)) [ ar_2 >= 2 ]
7.62/3.69	
7.62/3.69			(Comp: 2, Cost: 1)    evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_2 ]
7.62/3.69	
7.62/3.69			(Comp: 2, Cost: 1)    evalwcet1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1stop(ar_0, ar_1, ar_2, ar_3))
7.62/3.69	
7.62/3.69			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
7.62/3.69	
7.62/3.69		start location:	koat_start
7.62/3.69	
7.62/3.69		leaf cost:	0
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	A polynomial rank function with
7.62/3.69	
7.62/3.69		Pol(evalwcet1bbin) = V_3
7.62/3.69	
7.62/3.69		Pol(evalwcet1bb4in) = V_3
7.62/3.69	
7.62/3.69		Pol(evalwcet1bb1in) = V_3
7.62/3.69	
7.62/3.69		Pol(evalwcet1bb6in) = V_3
7.62/3.69	
7.62/3.69		Pol(evalwcet1bb5in) = V_3
7.62/3.69	
7.62/3.69	and size complexities
7.62/3.69	
7.62/3.69		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
7.62/3.69	
7.62/3.69		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
7.62/3.69	
7.62/3.69		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
7.62/3.69	
7.62/3.69		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
7.62/3.69	
7.62/3.69		S("evalwcet1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_0 + ar_2
7.62/3.69	
7.62/3.69		S("evalwcet1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_2 ]", 0-0) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_2 ]", 0-1) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_2 ]", 0-2) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_2 ]", 0-3) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, ar_3, ar_2 - 1, ar_3)) [ ar_2 >= 2 ]", 0-0) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, ar_3, ar_2 - 1, ar_3)) [ ar_2 >= 2 ]", 0-1) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, ar_3, ar_2 - 1, ar_3)) [ ar_2 >= 2 ]", 0-2) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, ar_3, ar_2 - 1, ar_3)) [ ar_2 >= 2 ]", 0-3) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0))", 0-0) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0))", 0-1) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0))", 0-2) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0))", 0-3) = 0
7.62/3.69	
7.62/3.69		S("evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 - 1)) [ ar_1 >= 2 ]", 0-0) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 - 1)) [ ar_1 >= 2 ]", 0-1) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 - 1)) [ ar_1 >= 2 ]", 0-2) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 - 1)) [ ar_1 >= 2 ]", 0-3) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]", 0-0) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]", 0-1) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]", 0-2) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]", 0-3) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 + 1)) [ ar_0 >= ar_1 + 2 ]", 0-0) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 + 1)) [ ar_0 >= ar_1 + 2 ]", 0-1) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 + 1)) [ ar_0 >= ar_1 + 2 ]", 0-2) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 + 1)) [ ar_0 >= ar_1 + 2 ]", 0-3) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0)) [ ar_1 + 1 >= ar_0 ]", 0-0) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0)) [ ar_1 + 1 >= ar_0 ]", 0-1) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0)) [ ar_1 + 1 >= ar_0 ]", 0-2) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0)) [ ar_1 + 1 >= ar_0 ]", 0-3) = 0
7.62/3.69	
7.62/3.69		S("evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]", 0-0) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]", 0-1) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]", 0-2) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]", 0-3) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]", 0-0) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]", 0-1) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]", 0-2) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]", 0-3) = ?
7.62/3.69	
7.62/3.69		S("evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1
7.62/3.69	
7.62/3.69		S("evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2
7.62/3.69	
7.62/3.69		S("evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3
7.62/3.69	
7.62/3.69		S("evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, 0, ar_0, ar_3)) [ ar_0 >= 1 ]", 0-0) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, 0, ar_0, ar_3)) [ ar_0 >= 1 ]", 0-1) = 0
7.62/3.69	
7.62/3.69		S("evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, 0, ar_0, ar_3)) [ ar_0 >= 1 ]", 0-2) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, 0, ar_0, ar_3)) [ ar_0 >= 1 ]", 0-3) = ar_3
7.62/3.69	
7.62/3.69		S("evalwcet1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1entryin(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
7.62/3.69	
7.62/3.69		S("evalwcet1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1entryin(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
7.62/3.69	
7.62/3.69		S("evalwcet1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1entryin(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
7.62/3.69	
7.62/3.69		S("evalwcet1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1entryin(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
7.62/3.69	
7.62/3.69	orients the transitions
7.62/3.69	
7.62/3.69		evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3))
7.62/3.69	
7.62/3.69		evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
7.62/3.69	
7.62/3.69		evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
7.62/3.69	
7.62/3.69		evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, ar_3, ar_2 - 1, ar_3)) [ ar_2 >= 2 ]
7.62/3.69	
7.62/3.69		evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0))
7.62/3.69	
7.62/3.69		evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 - 1)) [ ar_1 >= 2 ]
7.62/3.69	
7.62/3.69		evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]
7.62/3.69	
7.62/3.69		evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 + 1)) [ ar_0 >= ar_1 + 2 ]
7.62/3.69	
7.62/3.69		evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0)) [ ar_1 + 1 >= ar_0 ]
7.62/3.69	
7.62/3.69	weakly and the transition
7.62/3.69	
7.62/3.69		evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, ar_3, ar_2 - 1, ar_3)) [ ar_2 >= 2 ]
7.62/3.69	
7.62/3.69	strictly and produces the following problem:
7.62/3.69	
7.62/3.69	4:	T:
7.62/3.69	
7.62/3.69			(Comp: 1, Cost: 1)       evalwcet1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1entryin(ar_0, ar_1, ar_2, ar_3))
7.62/3.69	
7.62/3.69			(Comp: 1, Cost: 1)       evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, 0, ar_0, ar_3)) [ ar_0 >= 1 ]
7.62/3.69	
7.62/3.69			(Comp: 1, Cost: 1)       evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)       evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)       evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)       evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3))
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)       evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0)) [ ar_1 + 1 >= ar_0 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)       evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 + 1)) [ ar_0 >= ar_1 + 2 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)       evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)       evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 - 1)) [ ar_1 >= 2 ]
7.62/3.69	
7.62/3.69			(Comp: ?, Cost: 1)       evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0))
7.62/3.69	
7.62/3.69			(Comp: ar_0, Cost: 1)    evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, ar_3, ar_2 - 1, ar_3)) [ ar_2 >= 2 ]
7.62/3.69	
7.62/3.69			(Comp: 2, Cost: 1)       evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_2 ]
7.62/3.69	
7.62/3.69			(Comp: 2, Cost: 1)       evalwcet1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1stop(ar_0, ar_1, ar_2, ar_3))
7.62/3.69	
7.62/3.69			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
7.62/3.69	
7.62/3.69		start location:	koat_start
7.62/3.69	
7.62/3.69		leaf cost:	0
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Repeatedly propagating knowledge in problem 4 produces the following problem:
7.62/3.69	
7.62/3.69	5:	T:
7.62/3.69	
7.62/3.69			(Comp: 1, Cost: 1)             evalwcet1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1entryin(ar_0, ar_1, ar_2, ar_3))
7.62/3.69	
7.62/3.69			(Comp: 1, Cost: 1)             evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, 0, ar_0, ar_3)) [ ar_0 >= 1 ]
7.62/3.69	
7.62/3.69			(Comp: 1, Cost: 1)             evalwcet1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
7.62/3.69	
7.62/3.69			(Comp: ar_0 + 1, Cost: 1)      evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
7.62/3.69	
7.62/3.69			(Comp: ar_0 + 1, Cost: 1)      evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
7.62/3.69	
7.62/3.69			(Comp: ar_0 + 1, Cost: 1)      evalwcet1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3))
7.62/3.69	
7.62/3.69			(Comp: 2*ar_0 + 2, Cost: 1)    evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0)) [ ar_1 + 1 >= ar_0 ]
7.62/3.69	
7.62/3.69			(Comp: 2*ar_0 + 2, Cost: 1)    evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 + 1)) [ ar_0 >= ar_1 + 2 ]
7.62/3.69	
7.62/3.69			(Comp: ar_0 + 1, Cost: 1)      evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]
7.62/3.69	
7.62/3.69			(Comp: ar_0 + 1, Cost: 1)      evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, ar_1 - 1)) [ ar_1 >= 2 ]
7.62/3.69	
7.62/3.69			(Comp: ar_0 + 1, Cost: 1)      evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bb6in(ar_0, ar_1, ar_2, 0))
7.62/3.69	
7.62/3.69			(Comp: ar_0, Cost: 1)          evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1bbin(ar_0, ar_3, ar_2 - 1, ar_3)) [ ar_2 >= 2 ]
7.62/3.69	
7.62/3.69			(Comp: 2, Cost: 1)             evalwcet1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1returnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_2 ]
7.62/3.69	
7.62/3.69			(Comp: 2, Cost: 1)             evalwcet1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1stop(ar_0, ar_1, ar_2, ar_3))
7.62/3.69	
7.62/3.69			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
7.62/3.69	
7.62/3.69		start location:	koat_start
7.62/3.69	
7.62/3.69		leaf cost:	0
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Complexity upper bound 11*ar_0 + 17
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Time: 0.173 sec (SMT: 0.150 sec)
7.62/3.69	
7.62/3.69	
7.62/3.69	----------------------------------------
7.62/3.69	
7.62/3.69	(2)
7.62/3.69	BOUNDS(1, n^1)
7.62/3.69	
7.62/3.69	----------------------------------------
7.62/3.69	
7.62/3.69	(3) Loat Proof (FINISHED)
7.62/3.69	
7.62/3.69	
7.62/3.69	### Pre-processing the ITS problem ###
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Initial linear ITS problem
7.62/3.69	
7.62/3.69	   Start location: evalwcet1start
7.62/3.69	
7.62/3.69	      0: evalwcet1start -> evalwcet1entryin : [], cost: 1
7.62/3.69	
7.62/3.69	      1: evalwcet1entryin -> evalwcet1bbin : B'=0, C'=A, [ A>=1 ], cost: 1
7.62/3.69	
7.62/3.69	      2: evalwcet1entryin -> evalwcet1returnin : [ 0>=A ], cost: 1
7.62/3.69	
7.62/3.69	      3: evalwcet1bbin -> evalwcet1bb1in : [ 0>=1+free ], cost: 1
7.62/3.69	
7.62/3.69	      4: evalwcet1bbin -> evalwcet1bb1in : [ free_1>=1 ], cost: 1
7.62/3.69	
7.62/3.69	      5: evalwcet1bbin -> evalwcet1bb4in : [], cost: 1
7.62/3.69	
7.62/3.69	      6: evalwcet1bb1in -> evalwcet1bb6in : D'=0, [ 1+B>=A ], cost: 1
7.62/3.69	
7.62/3.69	      7: evalwcet1bb1in -> evalwcet1bb6in : D'=1+B, [ A>=2+B ], cost: 1
7.62/3.69	
7.62/3.69	      8: evalwcet1bb4in -> evalwcet1bb5in : [ 1>=B ], cost: 1
7.62/3.69	
7.62/3.69	      9: evalwcet1bb4in -> evalwcet1bb6in : D'=-1+B, [ B>=2 ], cost: 1
7.62/3.69	
7.62/3.69	     10: evalwcet1bb5in -> evalwcet1bb6in : D'=0, [], cost: 1
7.62/3.69	
7.62/3.69	     11: evalwcet1bb6in -> evalwcet1bbin : B'=D, C'=-1+C, [ C>=2 ], cost: 1
7.62/3.69	
7.62/3.69	     12: evalwcet1bb6in -> evalwcet1returnin : [ 1>=C ], cost: 1
7.62/3.69	
7.62/3.69	     13: evalwcet1returnin -> evalwcet1stop : [], cost: 1
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Removed unreachable and leaf rules:
7.62/3.69	
7.62/3.69	   Start location: evalwcet1start
7.62/3.69	
7.62/3.69	      0: evalwcet1start -> evalwcet1entryin : [], cost: 1
7.62/3.69	
7.62/3.69	      1: evalwcet1entryin -> evalwcet1bbin : B'=0, C'=A, [ A>=1 ], cost: 1
7.62/3.69	
7.62/3.69	      3: evalwcet1bbin -> evalwcet1bb1in : [ 0>=1+free ], cost: 1
7.62/3.69	
7.62/3.69	      4: evalwcet1bbin -> evalwcet1bb1in : [ free_1>=1 ], cost: 1
7.62/3.69	
7.62/3.69	      5: evalwcet1bbin -> evalwcet1bb4in : [], cost: 1
7.62/3.69	
7.62/3.69	      6: evalwcet1bb1in -> evalwcet1bb6in : D'=0, [ 1+B>=A ], cost: 1
7.62/3.69	
7.62/3.69	      7: evalwcet1bb1in -> evalwcet1bb6in : D'=1+B, [ A>=2+B ], cost: 1
7.62/3.69	
7.62/3.69	      8: evalwcet1bb4in -> evalwcet1bb5in : [ 1>=B ], cost: 1
7.62/3.69	
7.62/3.69	      9: evalwcet1bb4in -> evalwcet1bb6in : D'=-1+B, [ B>=2 ], cost: 1
7.62/3.69	
7.62/3.69	     10: evalwcet1bb5in -> evalwcet1bb6in : D'=0, [], cost: 1
7.62/3.69	
7.62/3.69	     11: evalwcet1bb6in -> evalwcet1bbin : B'=D, C'=-1+C, [ C>=2 ], cost: 1
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Simplified all rules, resulting in:
7.62/3.69	
7.62/3.69	   Start location: evalwcet1start
7.62/3.69	
7.62/3.69	      0: evalwcet1start -> evalwcet1entryin : [], cost: 1
7.62/3.69	
7.62/3.69	      1: evalwcet1entryin -> evalwcet1bbin : B'=0, C'=A, [ A>=1 ], cost: 1
7.62/3.69	
7.62/3.69	      4: evalwcet1bbin -> evalwcet1bb1in : [], cost: 1
7.62/3.69	
7.62/3.69	      5: evalwcet1bbin -> evalwcet1bb4in : [], cost: 1
7.62/3.69	
7.62/3.69	      6: evalwcet1bb1in -> evalwcet1bb6in : D'=0, [ 1+B>=A ], cost: 1
7.62/3.69	
7.62/3.69	      7: evalwcet1bb1in -> evalwcet1bb6in : D'=1+B, [ A>=2+B ], cost: 1
7.62/3.69	
7.62/3.69	      8: evalwcet1bb4in -> evalwcet1bb5in : [ 1>=B ], cost: 1
7.62/3.69	
7.62/3.69	      9: evalwcet1bb4in -> evalwcet1bb6in : D'=-1+B, [ B>=2 ], cost: 1
7.62/3.69	
7.62/3.69	     10: evalwcet1bb5in -> evalwcet1bb6in : D'=0, [], cost: 1
7.62/3.69	
7.62/3.69	     11: evalwcet1bb6in -> evalwcet1bbin : B'=D, C'=-1+C, [ C>=2 ], cost: 1
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	### Simplification by acceleration and chaining ###
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Eliminated locations (on linear paths):
7.62/3.69	
7.62/3.69	   Start location: evalwcet1start
7.62/3.69	
7.62/3.69	     14: evalwcet1start -> evalwcet1bbin : B'=0, C'=A, [ A>=1 ], cost: 2
7.62/3.69	
7.62/3.69	      4: evalwcet1bbin -> evalwcet1bb1in : [], cost: 1
7.62/3.69	
7.62/3.69	      5: evalwcet1bbin -> evalwcet1bb4in : [], cost: 1
7.62/3.69	
7.62/3.69	      6: evalwcet1bb1in -> evalwcet1bb6in : D'=0, [ 1+B>=A ], cost: 1
7.62/3.69	
7.62/3.69	      7: evalwcet1bb1in -> evalwcet1bb6in : D'=1+B, [ A>=2+B ], cost: 1
7.62/3.69	
7.62/3.69	      9: evalwcet1bb4in -> evalwcet1bb6in : D'=-1+B, [ B>=2 ], cost: 1
7.62/3.69	
7.62/3.69	     15: evalwcet1bb4in -> evalwcet1bb6in : D'=0, [ 1>=B ], cost: 2
7.62/3.69	
7.62/3.69	     11: evalwcet1bb6in -> evalwcet1bbin : B'=D, C'=-1+C, [ C>=2 ], cost: 1
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Eliminated locations (on tree-shaped paths):
7.62/3.69	
7.62/3.69	   Start location: evalwcet1start
7.62/3.69	
7.62/3.69	     14: evalwcet1start -> evalwcet1bbin : B'=0, C'=A, [ A>=1 ], cost: 2
7.62/3.69	
7.62/3.69	     16: evalwcet1bbin -> evalwcet1bb6in : D'=0, [ 1+B>=A ], cost: 2
7.62/3.69	
7.62/3.69	     17: evalwcet1bbin -> evalwcet1bb6in : D'=1+B, [ A>=2+B ], cost: 2
7.62/3.69	
7.62/3.69	     18: evalwcet1bbin -> evalwcet1bb6in : D'=-1+B, [ B>=2 ], cost: 2
7.62/3.69	
7.62/3.69	     19: evalwcet1bbin -> evalwcet1bb6in : D'=0, [ 1>=B ], cost: 3
7.62/3.69	
7.62/3.69	     11: evalwcet1bb6in -> evalwcet1bbin : B'=D, C'=-1+C, [ C>=2 ], cost: 1
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Eliminated locations (on tree-shaped paths):
7.62/3.69	
7.62/3.69	   Start location: evalwcet1start
7.62/3.69	
7.62/3.69	     14: evalwcet1start -> evalwcet1bbin : B'=0, C'=A, [ A>=1 ], cost: 2
7.62/3.69	
7.62/3.69	     20: evalwcet1bbin -> evalwcet1bbin : B'=0, C'=-1+C, D'=0, [ 1+B>=A && C>=2 ], cost: 3
7.62/3.69	
7.62/3.69	     21: evalwcet1bbin -> evalwcet1bbin : B'=1+B, C'=-1+C, D'=1+B, [ A>=2+B && C>=2 ], cost: 3
7.62/3.69	
7.62/3.69	     22: evalwcet1bbin -> evalwcet1bbin : B'=-1+B, C'=-1+C, D'=-1+B, [ B>=2 && C>=2 ], cost: 3
7.62/3.69	
7.62/3.69	     23: evalwcet1bbin -> evalwcet1bbin : B'=0, C'=-1+C, D'=0, [ 1>=B && C>=2 ], cost: 4
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Accelerating simple loops of location 2.
7.62/3.69	
7.62/3.69	   Accelerating the following rules:
7.62/3.69	
7.62/3.69	     20: evalwcet1bbin -> evalwcet1bbin : B'=0, C'=-1+C, D'=0, [ 1+B>=A && C>=2 ], cost: 3
7.62/3.69	
7.62/3.69	     21: evalwcet1bbin -> evalwcet1bbin : B'=1+B, C'=-1+C, D'=1+B, [ A>=2+B && C>=2 ], cost: 3
7.62/3.69	
7.62/3.69	     22: evalwcet1bbin -> evalwcet1bbin : B'=-1+B, C'=-1+C, D'=-1+B, [ B>=2 && C>=2 ], cost: 3
7.62/3.69	
7.62/3.69	     23: evalwcet1bbin -> evalwcet1bbin : B'=0, C'=-1+C, D'=0, [ 1>=B && C>=2 ], cost: 4
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	   Accelerated rule 20 with metering function -1+C (after strengthening guard), yielding the new rule 24.
7.62/3.69	
7.62/3.69	   Accelerated rule 21 with backward acceleration, yielding the new rule 25.
7.62/3.69	
7.62/3.69	   Accelerated rule 21 with backward acceleration, yielding the new rule 26.
7.62/3.69	
7.62/3.69	   Accelerated rule 22 with metering function -1+C (after adding B>=C), yielding the new rule 27.
7.62/3.69	
7.62/3.69	   Accelerated rule 22 with metering function -1+B (after adding B<=C), yielding the new rule 28.
7.62/3.69	
7.62/3.69	   Accelerated rule 23 with metering function -1+C, yielding the new rule 29.
7.62/3.69	
7.62/3.69	   Removing the simple loops: 21 22 23.
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Accelerated all simple loops using metering functions (where possible):
7.62/3.69	
7.62/3.69	   Start location: evalwcet1start
7.62/3.69	
7.62/3.69	     14: evalwcet1start -> evalwcet1bbin : B'=0, C'=A, [ A>=1 ], cost: 2
7.62/3.69	
7.62/3.69	     20: evalwcet1bbin -> evalwcet1bbin : B'=0, C'=-1+C, D'=0, [ 1+B>=A && C>=2 ], cost: 3
7.62/3.69	
7.62/3.69	     24: evalwcet1bbin -> evalwcet1bbin : B'=0, C'=1, D'=0, [ 1+B>=A && C>=2 && 1>=A ], cost: -3+3*C
7.62/3.69	
7.62/3.69	     25: evalwcet1bbin -> evalwcet1bbin : B'=-1+A, C'=1+C-A+B, D'=-1+A, [ A>=2+B && C>=2 && 2+C-A+B>=2 ], cost: -3+3*A-3*B
7.62/3.69	
7.62/3.69	     26: evalwcet1bbin -> evalwcet1bbin : B'=-1+C+B, C'=1, D'=-1+C+B, [ A>=2+B && C>=2 && A>=C+B ], cost: -3+3*C
7.62/3.69	
7.62/3.69	     27: evalwcet1bbin -> evalwcet1bbin : B'=1-C+B, C'=1, D'=1-C+B, [ B>=2 && C>=2 && B>=C ], cost: -3+3*C
7.62/3.69	
7.62/3.69	     28: evalwcet1bbin -> evalwcet1bbin : B'=1, C'=1+C-B, D'=1, [ B>=2 && C>=2 && B<=C ], cost: -3+3*B
7.62/3.69	
7.62/3.69	     29: evalwcet1bbin -> evalwcet1bbin : B'=0, C'=1, D'=0, [ 1>=B && C>=2 ], cost: -4+4*C
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Chained accelerated rules (with incoming rules):
7.62/3.69	
7.62/3.69	   Start location: evalwcet1start
7.62/3.69	
7.62/3.69	     14: evalwcet1start -> evalwcet1bbin : B'=0, C'=A, [ A>=1 ], cost: 2
7.62/3.69	
7.62/3.69	     30: evalwcet1start -> evalwcet1bbin : B'=-1+A, C'=1, D'=-1+A, [ A>=2 ], cost: -1+3*A
7.62/3.69	
7.62/3.69	     31: evalwcet1start -> evalwcet1bbin : B'=-1+A, C'=1, D'=-1+A, [ A>=2 ], cost: -1+3*A
7.62/3.69	
7.62/3.69	     32: evalwcet1start -> evalwcet1bbin : B'=0, C'=1, D'=0, [ A>=2 ], cost: -2+4*A
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Removed unreachable locations (and leaf rules with constant cost):
7.62/3.69	
7.62/3.69	   Start location: evalwcet1start
7.62/3.69	
7.62/3.69	     30: evalwcet1start -> evalwcet1bbin : B'=-1+A, C'=1, D'=-1+A, [ A>=2 ], cost: -1+3*A
7.62/3.69	
7.62/3.69	     31: evalwcet1start -> evalwcet1bbin : B'=-1+A, C'=1, D'=-1+A, [ A>=2 ], cost: -1+3*A
7.62/3.69	
7.62/3.69	     32: evalwcet1start -> evalwcet1bbin : B'=0, C'=1, D'=0, [ A>=2 ], cost: -2+4*A
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	### Computing asymptotic complexity ###
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Fully simplified ITS problem
7.62/3.69	
7.62/3.69	   Start location: evalwcet1start
7.62/3.69	
7.62/3.69	     31: evalwcet1start -> evalwcet1bbin : B'=-1+A, C'=1, D'=-1+A, [ A>=2 ], cost: -1+3*A
7.62/3.69	
7.62/3.69	     32: evalwcet1start -> evalwcet1bbin : B'=0, C'=1, D'=0, [ A>=2 ], cost: -2+4*A
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Computing asymptotic complexity for rule 31
7.62/3.69	
7.62/3.69	   Solved the limit problem by the following transformations:
7.62/3.69	
7.62/3.69	      Created initial limit problem:
7.62/3.69	
7.62/3.69	      -1+A (+/+!), -1+3*A (+) [not solved]
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	      removing all constraints (solved by SMT)
7.62/3.69	
7.62/3.69	      resulting limit problem: [solved]
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	      applying transformation rule (C) using substitution {A==n}
7.62/3.69	
7.62/3.69	      resulting limit problem:
7.62/3.69	
7.62/3.69	      [solved]
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	   Solution:
7.62/3.69	
7.62/3.69	      A / n
7.62/3.69	
7.62/3.69	   Resulting cost -1+3*n has complexity: Poly(n^1)
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Found new complexity Poly(n^1).
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	Obtained the following overall complexity (w.r.t. the length of the input n):
7.62/3.69	
7.62/3.69	   Complexity:  Poly(n^1)
7.62/3.69	
7.62/3.69	   Cpx degree:  1
7.62/3.69	
7.62/3.69	   Solved cost: -1+3*n
7.62/3.69	
7.62/3.69	   Rule cost:   -1+3*A
7.62/3.69	
7.62/3.69	   Rule guard:  [ A>=2 ]
7.62/3.69	
7.62/3.69	
7.62/3.69	
7.62/3.69	WORST_CASE(Omega(n^1),?)
7.62/3.69	
7.62/3.69	
7.62/3.69	----------------------------------------
7.62/3.69	
7.62/3.69	(4)
7.62/3.69	BOUNDS(n^1, INF)
7.73/3.72	EOF