4.50/2.22	WORST_CASE(Omega(n^1), O(n^1))
4.50/2.22	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.50/2.22	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.50/2.22	
4.50/2.22	
4.50/2.22	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
4.50/2.22	
4.50/2.22	(0) CpxIntTrs
4.50/2.22	(1) Koat Proof [FINISHED, 26 ms]
4.50/2.22	(2) BOUNDS(1, n^1)
4.50/2.22	(3) Loat Proof [FINISHED, 626 ms]
4.50/2.22	(4) BOUNDS(n^1, INF)
4.50/2.22	
4.50/2.22	
4.50/2.22	----------------------------------------
4.50/2.22	
4.50/2.22	(0)
4.50/2.22	Obligation:
4.50/2.22	Complexity Int TRS consisting of the following rules:
4.50/2.22	evalwcet2start(A, B) -> Com_1(evalwcet2entryin(A, B)) :|: TRUE
4.50/2.22	evalwcet2entryin(A, B) -> Com_1(evalwcet2bb5in(A, B)) :|: TRUE
4.50/2.22	evalwcet2bb5in(A, B) -> Com_1(evalwcet2bb2in(A, 0)) :|: 4 >= A
4.50/2.22	evalwcet2bb5in(A, B) -> Com_1(evalwcet2returnin(A, B)) :|: A >= 5
4.50/2.22	evalwcet2bb2in(A, B) -> Com_1(evalwcet2bb1in(A, B)) :|: A >= 3 && 9 >= B
4.50/2.22	evalwcet2bb2in(A, B) -> Com_1(evalwcet2bb4in(A, B)) :|: 2 >= A
4.50/2.22	evalwcet2bb2in(A, B) -> Com_1(evalwcet2bb4in(A, B)) :|: B >= 10
4.50/2.22	evalwcet2bb1in(A, B) -> Com_1(evalwcet2bb2in(A, B + 1)) :|: TRUE
4.50/2.22	evalwcet2bb4in(A, B) -> Com_1(evalwcet2bb5in(A + 1, B)) :|: TRUE
4.50/2.22	evalwcet2returnin(A, B) -> Com_1(evalwcet2stop(A, B)) :|: TRUE
4.50/2.22	
4.50/2.22	The start-symbols are:[evalwcet2start_2]
4.50/2.22	
4.50/2.22	
4.50/2.22	----------------------------------------
4.50/2.22	
4.50/2.22	(1) Koat Proof (FINISHED)
4.50/2.22	YES(?, 56*ar_0 + 258)
4.50/2.22	
4.50/2.22	
4.50/2.22	
4.50/2.22	Initial complexity problem:
4.50/2.22	
4.50/2.22	1:	T:
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2start(ar_0, ar_1) -> Com_1(evalwcet2entryin(ar_0, ar_1))
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2entryin(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0, ar_1))
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, 0)) [ 4 >= ar_0 ]
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2returnin(ar_0, ar_1)) [ ar_0 >= 5 ]
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb1in(ar_0, ar_1)) [ ar_0 >= 3 /\ 9 >= ar_1 ]
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ 2 >= ar_0 ]
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ ar_1 >= 10 ]
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2bb1in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, ar_1 + 1))
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2bb4in(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0 + 1, ar_1))
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2returnin(ar_0, ar_1) -> Com_1(evalwcet2stop(ar_0, ar_1))
4.50/2.22	
4.50/2.22			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalwcet2start(ar_0, ar_1)) [ 0 <= 0 ]
4.50/2.22	
4.50/2.22		start location:	koat_start
4.50/2.22	
4.50/2.22		leaf cost:	0
4.50/2.22	
4.50/2.22	
4.50/2.22	
4.50/2.22	Repeatedly propagating knowledge in problem 1 produces the following problem:
4.50/2.22	
4.50/2.22	2:	T:
4.50/2.22	
4.50/2.22			(Comp: 1, Cost: 1)    evalwcet2start(ar_0, ar_1) -> Com_1(evalwcet2entryin(ar_0, ar_1))
4.50/2.22	
4.50/2.22			(Comp: 1, Cost: 1)    evalwcet2entryin(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0, ar_1))
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, 0)) [ 4 >= ar_0 ]
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2returnin(ar_0, ar_1)) [ ar_0 >= 5 ]
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb1in(ar_0, ar_1)) [ ar_0 >= 3 /\ 9 >= ar_1 ]
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ 2 >= ar_0 ]
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ ar_1 >= 10 ]
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2bb1in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, ar_1 + 1))
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2bb4in(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0 + 1, ar_1))
4.50/2.22	
4.50/2.22			(Comp: ?, Cost: 1)    evalwcet2returnin(ar_0, ar_1) -> Com_1(evalwcet2stop(ar_0, ar_1))
4.50/2.22	
4.50/2.22			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalwcet2start(ar_0, ar_1)) [ 0 <= 0 ]
4.50/2.22	
4.50/2.22		start location:	koat_start
4.50/2.22	
4.50/2.22		leaf cost:	0
4.50/2.22	
4.50/2.22	
4.50/2.22	
4.50/2.22	A polynomial rank function with
4.50/2.22	
4.50/2.22		Pol(evalwcet2start) = 2
4.50/2.22	
4.50/2.22		Pol(evalwcet2entryin) = 2
4.50/2.22	
4.50/2.22		Pol(evalwcet2bb5in) = 2
4.50/2.22	
4.50/2.22		Pol(evalwcet2bb2in) = 2
4.50/2.22	
4.50/2.22		Pol(evalwcet2returnin) = 1
4.50/2.22	
4.50/2.22		Pol(evalwcet2bb1in) = 2
4.50/2.22	
4.50/2.22		Pol(evalwcet2bb4in) = 2
4.50/2.22	
4.50/2.22		Pol(evalwcet2stop) = 0
4.50/2.22	
4.50/2.22		Pol(koat_start) = 2
4.50/2.22	
4.50/2.22	orients all transitions weakly and the transitions
4.50/2.22	
4.50/2.22		evalwcet2returnin(ar_0, ar_1) -> Com_1(evalwcet2stop(ar_0, ar_1))
4.50/2.22	
4.50/2.22		evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2returnin(ar_0, ar_1)) [ ar_0 >= 5 ]
4.50/2.23	
4.50/2.23	strictly and produces the following problem:
4.50/2.23	
4.50/2.23	3:	T:
4.50/2.23	
4.50/2.23			(Comp: 1, Cost: 1)    evalwcet2start(ar_0, ar_1) -> Com_1(evalwcet2entryin(ar_0, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 1, Cost: 1)    evalwcet2entryin(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0, ar_1))
4.50/2.23	
4.50/2.23			(Comp: ?, Cost: 1)    evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, 0)) [ 4 >= ar_0 ]
4.50/2.23	
4.50/2.23			(Comp: 2, Cost: 1)    evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2returnin(ar_0, ar_1)) [ ar_0 >= 5 ]
4.50/2.23	
4.50/2.23			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb1in(ar_0, ar_1)) [ ar_0 >= 3 /\ 9 >= ar_1 ]
4.50/2.23	
4.50/2.23			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ 2 >= ar_0 ]
4.50/2.23	
4.50/2.23			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ ar_1 >= 10 ]
4.50/2.23	
4.50/2.23			(Comp: ?, Cost: 1)    evalwcet2bb1in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, ar_1 + 1))
4.50/2.23	
4.50/2.23			(Comp: ?, Cost: 1)    evalwcet2bb4in(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0 + 1, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 2, Cost: 1)    evalwcet2returnin(ar_0, ar_1) -> Com_1(evalwcet2stop(ar_0, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalwcet2start(ar_0, ar_1)) [ 0 <= 0 ]
4.50/2.23	
4.50/2.23		start location:	koat_start
4.50/2.23	
4.50/2.23		leaf cost:	0
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	A polynomial rank function with
4.50/2.23	
4.50/2.23		Pol(evalwcet2start) = -2*V_1 + 9
4.50/2.23	
4.50/2.23		Pol(evalwcet2entryin) = -2*V_1 + 9
4.50/2.23	
4.50/2.23		Pol(evalwcet2bb5in) = -2*V_1 + 9
4.50/2.23	
4.50/2.23		Pol(evalwcet2bb2in) = -2*V_1 + 8
4.50/2.23	
4.50/2.23		Pol(evalwcet2returnin) = -2*V_1
4.50/2.23	
4.50/2.23		Pol(evalwcet2bb1in) = -2*V_1 + 8
4.50/2.23	
4.50/2.23		Pol(evalwcet2bb4in) = -2*V_1 + 7
4.50/2.23	
4.50/2.23		Pol(evalwcet2stop) = -2*V_1
4.50/2.23	
4.50/2.23		Pol(koat_start) = -2*V_1 + 9
4.50/2.23	
4.50/2.23	orients all transitions weakly and the transitions
4.50/2.23	
4.50/2.23		evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, 0)) [ 4 >= ar_0 ]
4.50/2.23	
4.50/2.23		evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ 2 >= ar_0 ]
4.50/2.23	
4.50/2.23	strictly and produces the following problem:
4.50/2.23	
4.50/2.23	4:	T:
4.50/2.23	
4.50/2.23			(Comp: 1, Cost: 1)             evalwcet2start(ar_0, ar_1) -> Com_1(evalwcet2entryin(ar_0, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 1, Cost: 1)             evalwcet2entryin(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 2*ar_0 + 9, Cost: 1)    evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, 0)) [ 4 >= ar_0 ]
4.50/2.23	
4.50/2.23			(Comp: 2, Cost: 1)             evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2returnin(ar_0, ar_1)) [ ar_0 >= 5 ]
4.50/2.23	
4.50/2.23			(Comp: ?, Cost: 1)             evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb1in(ar_0, ar_1)) [ ar_0 >= 3 /\ 9 >= ar_1 ]
4.50/2.23	
4.50/2.23			(Comp: 2*ar_0 + 9, Cost: 1)    evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ 2 >= ar_0 ]
4.50/2.23	
4.50/2.23			(Comp: ?, Cost: 1)             evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ ar_1 >= 10 ]
4.50/2.23	
4.50/2.23			(Comp: ?, Cost: 1)             evalwcet2bb1in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, ar_1 + 1))
4.50/2.23	
4.50/2.23			(Comp: ?, Cost: 1)             evalwcet2bb4in(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0 + 1, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 2, Cost: 1)             evalwcet2returnin(ar_0, ar_1) -> Com_1(evalwcet2stop(ar_0, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1) -> Com_1(evalwcet2start(ar_0, ar_1)) [ 0 <= 0 ]
4.50/2.23	
4.50/2.23		start location:	koat_start
4.50/2.23	
4.50/2.23		leaf cost:	0
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	A polynomial rank function with
4.50/2.23	
4.50/2.23		Pol(evalwcet2bb4in) = 1
4.50/2.23	
4.50/2.23		Pol(evalwcet2bb5in) = 0
4.50/2.23	
4.50/2.23		Pol(evalwcet2bb2in) = 2
4.50/2.23	
4.50/2.23		Pol(evalwcet2bb1in) = 2
4.50/2.23	
4.50/2.23	and size complexities
4.50/2.23	
4.50/2.23		S("koat_start(ar_0, ar_1) -> Com_1(evalwcet2start(ar_0, ar_1)) [ 0 <= 0 ]", 0-0) = ar_0
4.50/2.23	
4.50/2.23		S("koat_start(ar_0, ar_1) -> Com_1(evalwcet2start(ar_0, ar_1)) [ 0 <= 0 ]", 0-1) = ar_1
4.50/2.23	
4.50/2.23		S("evalwcet2returnin(ar_0, ar_1) -> Com_1(evalwcet2stop(ar_0, ar_1))", 0-0) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2returnin(ar_0, ar_1) -> Com_1(evalwcet2stop(ar_0, ar_1))", 0-1) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb4in(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0 + 1, ar_1))", 0-0) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb4in(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0 + 1, ar_1))", 0-1) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb1in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, ar_1 + 1))", 0-0) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb1in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, ar_1 + 1))", 0-1) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ ar_1 >= 10 ]", 0-0) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ ar_1 >= 10 ]", 0-1) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ 2 >= ar_0 ]", 0-0) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ 2 >= ar_0 ]", 0-1) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb1in(ar_0, ar_1)) [ ar_0 >= 3 /\\ 9 >= ar_1 ]", 0-0) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb1in(ar_0, ar_1)) [ ar_0 >= 3 /\\ 9 >= ar_1 ]", 0-1) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2returnin(ar_0, ar_1)) [ ar_0 >= 5 ]", 0-0) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2returnin(ar_0, ar_1)) [ ar_0 >= 5 ]", 0-1) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, 0)) [ 4 >= ar_0 ]", 0-0) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, 0)) [ 4 >= ar_0 ]", 0-1) = 0
4.50/2.23	
4.50/2.23		S("evalwcet2entryin(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0, ar_1))", 0-0) = ar_0
4.50/2.23	
4.50/2.23		S("evalwcet2entryin(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0, ar_1))", 0-1) = ar_1
4.50/2.23	
4.50/2.23		S("evalwcet2start(ar_0, ar_1) -> Com_1(evalwcet2entryin(ar_0, ar_1))", 0-0) = ar_0
4.50/2.23	
4.50/2.23		S("evalwcet2start(ar_0, ar_1) -> Com_1(evalwcet2entryin(ar_0, ar_1))", 0-1) = ar_1
4.50/2.23	
4.50/2.23	orients the transitions
4.50/2.23	
4.50/2.23		evalwcet2bb4in(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0 + 1, ar_1))
4.50/2.23	
4.50/2.23		evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ ar_1 >= 10 ]
4.50/2.23	
4.50/2.23		evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb1in(ar_0, ar_1)) [ ar_0 >= 3 /\ 9 >= ar_1 ]
4.50/2.23	
4.50/2.23		evalwcet2bb1in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, ar_1 + 1))
4.50/2.23	
4.50/2.23	weakly and the transitions
4.50/2.23	
4.50/2.23		evalwcet2bb4in(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0 + 1, ar_1))
4.50/2.23	
4.50/2.23		evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ ar_1 >= 10 ]
4.50/2.23	
4.50/2.23	strictly and produces the following problem:
4.50/2.23	
4.50/2.23	5:	T:
4.50/2.23	
4.50/2.23			(Comp: 1, Cost: 1)              evalwcet2start(ar_0, ar_1) -> Com_1(evalwcet2entryin(ar_0, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 1, Cost: 1)              evalwcet2entryin(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 2*ar_0 + 9, Cost: 1)     evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, 0)) [ 4 >= ar_0 ]
4.50/2.23	
4.50/2.23			(Comp: 2, Cost: 1)              evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2returnin(ar_0, ar_1)) [ ar_0 >= 5 ]
4.50/2.23	
4.50/2.23			(Comp: ?, Cost: 1)              evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb1in(ar_0, ar_1)) [ ar_0 >= 3 /\ 9 >= ar_1 ]
4.50/2.23	
4.50/2.23			(Comp: 2*ar_0 + 9, Cost: 1)     evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ 2 >= ar_0 ]
4.50/2.23	
4.50/2.23			(Comp: 6*ar_0 + 27, Cost: 1)    evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ ar_1 >= 10 ]
4.50/2.23	
4.50/2.23			(Comp: ?, Cost: 1)              evalwcet2bb1in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, ar_1 + 1))
4.50/2.23	
4.50/2.23			(Comp: 6*ar_0 + 27, Cost: 1)    evalwcet2bb4in(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0 + 1, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 2, Cost: 1)              evalwcet2returnin(ar_0, ar_1) -> Com_1(evalwcet2stop(ar_0, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1) -> Com_1(evalwcet2start(ar_0, ar_1)) [ 0 <= 0 ]
4.50/2.23	
4.50/2.23		start location:	koat_start
4.50/2.23	
4.50/2.23		leaf cost:	0
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	A polynomial rank function with
4.50/2.23	
4.50/2.23		Pol(evalwcet2bb2in) = -V_2 + 10
4.50/2.23	
4.50/2.23		Pol(evalwcet2bb1in) = -V_2 + 9
4.50/2.23	
4.50/2.23	and size complexities
4.50/2.23	
4.50/2.23		S("koat_start(ar_0, ar_1) -> Com_1(evalwcet2start(ar_0, ar_1)) [ 0 <= 0 ]", 0-0) = ar_0
4.50/2.23	
4.50/2.23		S("koat_start(ar_0, ar_1) -> Com_1(evalwcet2start(ar_0, ar_1)) [ 0 <= 0 ]", 0-1) = ar_1
4.50/2.23	
4.50/2.23		S("evalwcet2returnin(ar_0, ar_1) -> Com_1(evalwcet2stop(ar_0, ar_1))", 0-0) = 7*ar_0 + 64827
4.50/2.23	
4.50/2.23		S("evalwcet2returnin(ar_0, ar_1) -> Com_1(evalwcet2stop(ar_0, ar_1))", 0-1) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb4in(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0 + 1, ar_1))", 0-0) = 7*ar_0 + 1323
4.50/2.23	
4.50/2.23		S("evalwcet2bb4in(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0 + 1, ar_1))", 0-1) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb1in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, ar_1 + 1))", 0-0) = 7*ar_0 + 1323
4.50/2.23	
4.50/2.23		S("evalwcet2bb1in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, ar_1 + 1))", 0-1) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ ar_1 >= 10 ]", 0-0) = 7*ar_0 + 1323
4.50/2.23	
4.50/2.23		S("evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ ar_1 >= 10 ]", 0-1) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ 2 >= ar_0 ]", 0-0) = 7*ar_0 + 1323
4.50/2.23	
4.50/2.23		S("evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ 2 >= ar_0 ]", 0-1) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb1in(ar_0, ar_1)) [ ar_0 >= 3 /\\ 9 >= ar_1 ]", 0-0) = 7*ar_0 + 1323
4.50/2.23	
4.50/2.23		S("evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb1in(ar_0, ar_1)) [ ar_0 >= 3 /\\ 9 >= ar_1 ]", 0-1) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2returnin(ar_0, ar_1)) [ ar_0 >= 5 ]", 0-0) = 7*ar_0 + 9261
4.50/2.23	
4.50/2.23		S("evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2returnin(ar_0, ar_1)) [ ar_0 >= 5 ]", 0-1) = ?
4.50/2.23	
4.50/2.23		S("evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, 0)) [ 4 >= ar_0 ]", 0-0) = 7*ar_0 + 1323
4.50/2.23	
4.50/2.23		S("evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, 0)) [ 4 >= ar_0 ]", 0-1) = 0
4.50/2.23	
4.50/2.23		S("evalwcet2entryin(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0, ar_1))", 0-0) = ar_0
4.50/2.23	
4.50/2.23		S("evalwcet2entryin(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0, ar_1))", 0-1) = ar_1
4.50/2.23	
4.50/2.23		S("evalwcet2start(ar_0, ar_1) -> Com_1(evalwcet2entryin(ar_0, ar_1))", 0-0) = ar_0
4.50/2.23	
4.50/2.23		S("evalwcet2start(ar_0, ar_1) -> Com_1(evalwcet2entryin(ar_0, ar_1))", 0-1) = ar_1
4.50/2.23	
4.50/2.23	orients the transitions
4.50/2.23	
4.50/2.23		evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb1in(ar_0, ar_1)) [ ar_0 >= 3 /\ 9 >= ar_1 ]
4.50/2.23	
4.50/2.23		evalwcet2bb1in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, ar_1 + 1))
4.50/2.23	
4.50/2.23	weakly and the transition
4.50/2.23	
4.50/2.23		evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb1in(ar_0, ar_1)) [ ar_0 >= 3 /\ 9 >= ar_1 ]
4.50/2.23	
4.50/2.23	strictly and produces the following problem:
4.50/2.23	
4.50/2.23	6:	T:
4.50/2.23	
4.50/2.23			(Comp: 1, Cost: 1)               evalwcet2start(ar_0, ar_1) -> Com_1(evalwcet2entryin(ar_0, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 1, Cost: 1)               evalwcet2entryin(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 2*ar_0 + 9, Cost: 1)      evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, 0)) [ 4 >= ar_0 ]
4.50/2.23	
4.50/2.23			(Comp: 2, Cost: 1)               evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2returnin(ar_0, ar_1)) [ ar_0 >= 5 ]
4.50/2.23	
4.50/2.23			(Comp: 20*ar_0 + 90, Cost: 1)    evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb1in(ar_0, ar_1)) [ ar_0 >= 3 /\ 9 >= ar_1 ]
4.50/2.23	
4.50/2.23			(Comp: 2*ar_0 + 9, Cost: 1)      evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ 2 >= ar_0 ]
4.50/2.23	
4.50/2.23			(Comp: 6*ar_0 + 27, Cost: 1)     evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ ar_1 >= 10 ]
4.50/2.23	
4.50/2.23			(Comp: ?, Cost: 1)               evalwcet2bb1in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, ar_1 + 1))
4.50/2.23	
4.50/2.23			(Comp: 6*ar_0 + 27, Cost: 1)     evalwcet2bb4in(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0 + 1, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 2, Cost: 1)               evalwcet2returnin(ar_0, ar_1) -> Com_1(evalwcet2stop(ar_0, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 1, Cost: 0)               koat_start(ar_0, ar_1) -> Com_1(evalwcet2start(ar_0, ar_1)) [ 0 <= 0 ]
4.50/2.23	
4.50/2.23		start location:	koat_start
4.50/2.23	
4.50/2.23		leaf cost:	0
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Repeatedly propagating knowledge in problem 6 produces the following problem:
4.50/2.23	
4.50/2.23	7:	T:
4.50/2.23	
4.50/2.23			(Comp: 1, Cost: 1)               evalwcet2start(ar_0, ar_1) -> Com_1(evalwcet2entryin(ar_0, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 1, Cost: 1)               evalwcet2entryin(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 2*ar_0 + 9, Cost: 1)      evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, 0)) [ 4 >= ar_0 ]
4.50/2.23	
4.50/2.23			(Comp: 2, Cost: 1)               evalwcet2bb5in(ar_0, ar_1) -> Com_1(evalwcet2returnin(ar_0, ar_1)) [ ar_0 >= 5 ]
4.50/2.23	
4.50/2.23			(Comp: 20*ar_0 + 90, Cost: 1)    evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb1in(ar_0, ar_1)) [ ar_0 >= 3 /\ 9 >= ar_1 ]
4.50/2.23	
4.50/2.23			(Comp: 2*ar_0 + 9, Cost: 1)      evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ 2 >= ar_0 ]
4.50/2.23	
4.50/2.23			(Comp: 6*ar_0 + 27, Cost: 1)     evalwcet2bb2in(ar_0, ar_1) -> Com_1(evalwcet2bb4in(ar_0, ar_1)) [ ar_1 >= 10 ]
4.50/2.23	
4.50/2.23			(Comp: 20*ar_0 + 90, Cost: 1)    evalwcet2bb1in(ar_0, ar_1) -> Com_1(evalwcet2bb2in(ar_0, ar_1 + 1))
4.50/2.23	
4.50/2.23			(Comp: 6*ar_0 + 27, Cost: 1)     evalwcet2bb4in(ar_0, ar_1) -> Com_1(evalwcet2bb5in(ar_0 + 1, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 2, Cost: 1)               evalwcet2returnin(ar_0, ar_1) -> Com_1(evalwcet2stop(ar_0, ar_1))
4.50/2.23	
4.50/2.23			(Comp: 1, Cost: 0)               koat_start(ar_0, ar_1) -> Com_1(evalwcet2start(ar_0, ar_1)) [ 0 <= 0 ]
4.50/2.23	
4.50/2.23		start location:	koat_start
4.50/2.23	
4.50/2.23		leaf cost:	0
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Complexity upper bound 56*ar_0 + 258
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Time: 0.088 sec (SMT: 0.078 sec)
4.50/2.23	
4.50/2.23	
4.50/2.23	----------------------------------------
4.50/2.23	
4.50/2.23	(2)
4.50/2.23	BOUNDS(1, n^1)
4.50/2.23	
4.50/2.23	----------------------------------------
4.50/2.23	
4.50/2.23	(3) Loat Proof (FINISHED)
4.50/2.23	
4.50/2.23	
4.50/2.23	### Pre-processing the ITS problem ###
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Initial linear ITS problem
4.50/2.23	
4.50/2.23	   Start location: evalwcet2start
4.50/2.23	
4.50/2.23	      0: evalwcet2start -> evalwcet2entryin : [], cost: 1
4.50/2.23	
4.50/2.23	      1: evalwcet2entryin -> evalwcet2bb5in : [], cost: 1
4.50/2.23	
4.50/2.23	      2: evalwcet2bb5in -> evalwcet2bb2in : B'=0, [ 4>=A ], cost: 1
4.50/2.23	
4.50/2.23	      3: evalwcet2bb5in -> evalwcet2returnin : [ A>=5 ], cost: 1
4.50/2.23	
4.50/2.23	      4: evalwcet2bb2in -> evalwcet2bb1in : [ A>=3 && 9>=B ], cost: 1
4.50/2.23	
4.50/2.23	      5: evalwcet2bb2in -> evalwcet2bb4in : [ 2>=A ], cost: 1
4.50/2.23	
4.50/2.23	      6: evalwcet2bb2in -> evalwcet2bb4in : [ B>=10 ], cost: 1
4.50/2.23	
4.50/2.23	      7: evalwcet2bb1in -> evalwcet2bb2in : B'=1+B, [], cost: 1
4.50/2.23	
4.50/2.23	      8: evalwcet2bb4in -> evalwcet2bb5in : A'=1+A, [], cost: 1
4.50/2.23	
4.50/2.23	      9: evalwcet2returnin -> evalwcet2stop : [], cost: 1
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Removed unreachable and leaf rules:
4.50/2.23	
4.50/2.23	   Start location: evalwcet2start
4.50/2.23	
4.50/2.23	      0: evalwcet2start -> evalwcet2entryin : [], cost: 1
4.50/2.23	
4.50/2.23	      1: evalwcet2entryin -> evalwcet2bb5in : [], cost: 1
4.50/2.23	
4.50/2.23	      2: evalwcet2bb5in -> evalwcet2bb2in : B'=0, [ 4>=A ], cost: 1
4.50/2.23	
4.50/2.23	      4: evalwcet2bb2in -> evalwcet2bb1in : [ A>=3 && 9>=B ], cost: 1
4.50/2.23	
4.50/2.23	      5: evalwcet2bb2in -> evalwcet2bb4in : [ 2>=A ], cost: 1
4.50/2.23	
4.50/2.23	      6: evalwcet2bb2in -> evalwcet2bb4in : [ B>=10 ], cost: 1
4.50/2.23	
4.50/2.23	      7: evalwcet2bb1in -> evalwcet2bb2in : B'=1+B, [], cost: 1
4.50/2.23	
4.50/2.23	      8: evalwcet2bb4in -> evalwcet2bb5in : A'=1+A, [], cost: 1
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	### Simplification by acceleration and chaining ###
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Eliminated locations (on linear paths):
4.50/2.23	
4.50/2.23	   Start location: evalwcet2start
4.50/2.23	
4.50/2.23	     10: evalwcet2start -> evalwcet2bb5in : [], cost: 2
4.50/2.23	
4.50/2.23	      2: evalwcet2bb5in -> evalwcet2bb2in : B'=0, [ 4>=A ], cost: 1
4.50/2.23	
4.50/2.23	      5: evalwcet2bb2in -> evalwcet2bb4in : [ 2>=A ], cost: 1
4.50/2.23	
4.50/2.23	      6: evalwcet2bb2in -> evalwcet2bb4in : [ B>=10 ], cost: 1
4.50/2.23	
4.50/2.23	     11: evalwcet2bb2in -> evalwcet2bb2in : B'=1+B, [ A>=3 && 9>=B ], cost: 2
4.50/2.23	
4.50/2.23	      8: evalwcet2bb4in -> evalwcet2bb5in : A'=1+A, [], cost: 1
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Accelerating simple loops of location 3.
4.50/2.23	
4.50/2.23	   Accelerating the following rules:
4.50/2.23	
4.50/2.23	     11: evalwcet2bb2in -> evalwcet2bb2in : B'=1+B, [ A>=3 && 9>=B ], cost: 2
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	   Accelerated rule 11 with metering function 10-B, yielding the new rule 12.
4.50/2.23	
4.50/2.23	   Removing the simple loops: 11.
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Accelerated all simple loops using metering functions (where possible):
4.50/2.23	
4.50/2.23	   Start location: evalwcet2start
4.50/2.23	
4.50/2.23	     10: evalwcet2start -> evalwcet2bb5in : [], cost: 2
4.50/2.23	
4.50/2.23	      2: evalwcet2bb5in -> evalwcet2bb2in : B'=0, [ 4>=A ], cost: 1
4.50/2.23	
4.50/2.23	      5: evalwcet2bb2in -> evalwcet2bb4in : [ 2>=A ], cost: 1
4.50/2.23	
4.50/2.23	      6: evalwcet2bb2in -> evalwcet2bb4in : [ B>=10 ], cost: 1
4.50/2.23	
4.50/2.23	     12: evalwcet2bb2in -> evalwcet2bb2in : B'=10, [ A>=3 && 9>=B ], cost: 20-2*B
4.50/2.23	
4.50/2.23	      8: evalwcet2bb4in -> evalwcet2bb5in : A'=1+A, [], cost: 1
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Chained accelerated rules (with incoming rules):
4.50/2.23	
4.50/2.23	   Start location: evalwcet2start
4.50/2.23	
4.50/2.23	     10: evalwcet2start -> evalwcet2bb5in : [], cost: 2
4.50/2.23	
4.50/2.23	      2: evalwcet2bb5in -> evalwcet2bb2in : B'=0, [ 4>=A ], cost: 1
4.50/2.23	
4.50/2.23	     13: evalwcet2bb5in -> evalwcet2bb2in : B'=10, [ 4>=A && A>=3 ], cost: 21
4.50/2.23	
4.50/2.23	      5: evalwcet2bb2in -> evalwcet2bb4in : [ 2>=A ], cost: 1
4.50/2.23	
4.50/2.23	      6: evalwcet2bb2in -> evalwcet2bb4in : [ B>=10 ], cost: 1
4.50/2.23	
4.50/2.23	      8: evalwcet2bb4in -> evalwcet2bb5in : A'=1+A, [], cost: 1
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Eliminated locations (on tree-shaped paths):
4.50/2.23	
4.50/2.23	   Start location: evalwcet2start
4.50/2.23	
4.50/2.23	     10: evalwcet2start -> evalwcet2bb5in : [], cost: 2
4.50/2.23	
4.50/2.23	     14: evalwcet2bb5in -> evalwcet2bb4in : B'=0, [ 2>=A ], cost: 2
4.50/2.23	
4.50/2.23	     15: evalwcet2bb5in -> evalwcet2bb4in : B'=10, [ 4>=A && A>=3 ], cost: 22
4.50/2.23	
4.50/2.23	      8: evalwcet2bb4in -> evalwcet2bb5in : A'=1+A, [], cost: 1
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Eliminated locations (on tree-shaped paths):
4.50/2.23	
4.50/2.23	   Start location: evalwcet2start
4.50/2.23	
4.50/2.23	     10: evalwcet2start -> evalwcet2bb5in : [], cost: 2
4.50/2.23	
4.50/2.23	     16: evalwcet2bb5in -> evalwcet2bb5in : A'=1+A, B'=0, [ 2>=A ], cost: 3
4.50/2.23	
4.50/2.23	     17: evalwcet2bb5in -> evalwcet2bb5in : A'=1+A, B'=10, [ 4>=A && A>=3 ], cost: 23
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Accelerating simple loops of location 2.
4.50/2.23	
4.50/2.23	   Accelerating the following rules:
4.50/2.23	
4.50/2.23	     16: evalwcet2bb5in -> evalwcet2bb5in : A'=1+A, B'=0, [ 2>=A ], cost: 3
4.50/2.23	
4.50/2.23	     17: evalwcet2bb5in -> evalwcet2bb5in : A'=1+A, B'=10, [ 4>=A && A>=3 ], cost: 23
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	   Accelerated rule 16 with metering function 3-A, yielding the new rule 18.
4.50/2.23	
4.50/2.23	   Accelerated rule 17 with metering function 5-A, yielding the new rule 19.
4.50/2.23	
4.50/2.23	   Removing the simple loops: 16 17.
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Accelerated all simple loops using metering functions (where possible):
4.50/2.23	
4.50/2.23	   Start location: evalwcet2start
4.50/2.23	
4.50/2.23	     10: evalwcet2start -> evalwcet2bb5in : [], cost: 2
4.50/2.23	
4.50/2.23	     18: evalwcet2bb5in -> evalwcet2bb5in : A'=3, B'=0, [ 2>=A ], cost: 9-3*A
4.50/2.23	
4.50/2.23	     19: evalwcet2bb5in -> evalwcet2bb5in : A'=5, B'=10, [ 4>=A && A>=3 ], cost: 115-23*A
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Chained accelerated rules (with incoming rules):
4.50/2.23	
4.50/2.23	   Start location: evalwcet2start
4.50/2.23	
4.50/2.23	     10: evalwcet2start -> evalwcet2bb5in : [], cost: 2
4.50/2.23	
4.50/2.23	     20: evalwcet2start -> evalwcet2bb5in : A'=3, B'=0, [ 2>=A ], cost: 11-3*A
4.50/2.23	
4.50/2.23	     21: evalwcet2start -> evalwcet2bb5in : A'=5, B'=10, [ 4>=A && A>=3 ], cost: 117-23*A
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Removed unreachable locations (and leaf rules with constant cost):
4.50/2.23	
4.50/2.23	   Start location: evalwcet2start
4.50/2.23	
4.50/2.23	     20: evalwcet2start -> evalwcet2bb5in : A'=3, B'=0, [ 2>=A ], cost: 11-3*A
4.50/2.23	
4.50/2.23	     21: evalwcet2start -> evalwcet2bb5in : A'=5, B'=10, [ 4>=A && A>=3 ], cost: 117-23*A
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	### Computing asymptotic complexity ###
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Fully simplified ITS problem
4.50/2.23	
4.50/2.23	   Start location: evalwcet2start
4.50/2.23	
4.50/2.23	     20: evalwcet2start -> evalwcet2bb5in : A'=3, B'=0, [ 2>=A ], cost: 11-3*A
4.50/2.23	
4.50/2.23	     21: evalwcet2start -> evalwcet2bb5in : A'=5, B'=10, [ 4>=A && A>=3 ], cost: 117-23*A
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Computing asymptotic complexity for rule 20
4.50/2.23	
4.50/2.23	   Solved the limit problem by the following transformations:
4.50/2.23	
4.50/2.23	      Created initial limit problem:
4.50/2.23	
4.50/2.23	      3-A (+/+!), 11-3*A (+) [not solved]
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	      removing all constraints (solved by SMT)
4.50/2.23	
4.50/2.23	      resulting limit problem: [solved]
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	      applying transformation rule (C) using substitution {A==-n}
4.50/2.23	
4.50/2.23	      resulting limit problem:
4.50/2.23	
4.50/2.23	      [solved]
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	   Solution:
4.50/2.23	
4.50/2.23	      A / -n
4.50/2.23	
4.50/2.23	   Resulting cost 11+3*n has complexity: Poly(n^1)
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Found new complexity Poly(n^1).
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	Obtained the following overall complexity (w.r.t. the length of the input n):
4.50/2.23	
4.50/2.23	   Complexity:  Poly(n^1)
4.50/2.23	
4.50/2.23	   Cpx degree:  1
4.50/2.23	
4.50/2.23	   Solved cost: 11+3*n
4.50/2.23	
4.50/2.23	   Rule cost:   11-3*A
4.50/2.23	
4.50/2.23	   Rule guard:  [ 2>=A ]
4.50/2.23	
4.50/2.23	
4.50/2.23	
4.50/2.23	WORST_CASE(Omega(n^1),?)
4.50/2.23	
4.50/2.23	
4.50/2.23	----------------------------------------
4.50/2.23	
4.50/2.23	(4)
4.50/2.23	BOUNDS(n^1, INF)
4.69/2.24	EOF