4.88/2.30	WORST_CASE(Omega(n^1), O(n^1))
4.88/2.31	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.88/2.31	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.88/2.31	
4.88/2.31	
4.88/2.31	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
4.88/2.31	
4.88/2.31	(0) CpxIntTrs
4.88/2.31	(1) Koat Proof [FINISHED, 131 ms]
4.88/2.31	(2) BOUNDS(1, n^1)
4.88/2.31	(3) Loat Proof [FINISHED, 626 ms]
4.88/2.31	(4) BOUNDS(n^1, INF)
4.88/2.31	
4.88/2.31	
4.88/2.31	----------------------------------------
4.88/2.31	
4.88/2.31	(0)
4.88/2.31	Obligation:
4.88/2.31	Complexity Int TRS consisting of the following rules:
4.88/2.31	eval_wise_start(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb0_in(v__0, v__01, v_x, v_y)) :|: TRUE
4.88/2.31	eval_wise_bb0_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_0(v__0, v__01, v_x, v_y)) :|: TRUE
4.88/2.31	eval_wise_0(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_1(v__0, v__01, v_x, v_y)) :|: TRUE
4.88/2.31	eval_wise_1(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_2(v__0, v__01, v_x, v_y)) :|: TRUE
4.88/2.31	eval_wise_2(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb2_in(v__0, v__01, v_x, v_y)) :|: v_x < 0
4.88/2.31	eval_wise_2(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb2_in(v__0, v__01, v_x, v_y)) :|: v_y < 0
4.88/2.31	eval_wise_2(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v_x, v_y, v_x, v_y)) :|: v_x >= 0 && v_y >= 0
4.88/2.31	eval_wise_bb1_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise__critedge_in(v__0, v__01, v_x, v_y)) :|: v__0 - v__01 > 2
4.88/2.31	eval_wise_bb1_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise__critedge_in(v__0, v__01, v_x, v_y)) :|: v__01 - v__0 > 2
4.88/2.31	eval_wise_bb1_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb2_in(v__0, v__01, v_x, v_y)) :|: v__0 - v__01 <= 2 && v__01 - v__0 <= 2
4.88/2.31	eval_wise__critedge_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v__0 + 1, v__01, v_x, v_y)) :|: v__0 < v__01
4.88/2.31	eval_wise__critedge_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v__0, v__01, v_x, v_y)) :|: v__0 < v__01 && v__0 >= v__01
4.88/2.31	eval_wise__critedge_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v__0 + 1, v__01 + 1, v_x, v_y)) :|: v__0 >= v__01 && v__0 < v__01
4.88/2.31	eval_wise__critedge_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v__0, v__01 + 1, v_x, v_y)) :|: v__0 >= v__01
4.88/2.31	eval_wise_bb2_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_stop(v__0, v__01, v_x, v_y)) :|: TRUE
4.88/2.31	
4.88/2.31	The start-symbols are:[eval_wise_start_4]
4.88/2.31	
4.88/2.31	
4.88/2.31	----------------------------------------
4.88/2.31	
4.88/2.31	(1) Koat Proof (FINISHED)
4.88/2.31	YES(?, 8*ar_0 + 8*ar_1 + 17)
4.88/2.31	
4.88/2.31	
4.88/2.31	
4.88/2.31	Initial complexity problem:
4.88/2.31	
4.88/2.31	1:	T:
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb0in(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise0(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwise0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise1(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwise1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise2(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\ ar_2 + 2 >= ar_3 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 /\ ar_2 >= ar_3 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3 + 1)) [ ar_2 >= ar_3 /\ ar_3 >= ar_2 + 1 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
4.88/2.31	
4.88/2.31		start location:	koat_start
4.88/2.31	
4.88/2.31		leaf cost:	0
4.88/2.31	
4.88/2.31	
4.88/2.31	
4.88/2.31	Testing for reachability in the complexity graph removes the following transitions from problem 1:
4.88/2.31	
4.88/2.31		evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 /\ ar_2 >= ar_3 ]
4.88/2.31	
4.88/2.31		evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3 + 1)) [ ar_2 >= ar_3 /\ ar_3 >= ar_2 + 1 ]
4.88/2.31	
4.88/2.31	We thus obtain the following problem:
4.88/2.31	
4.88/2.31	2:	T:
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\ ar_2 + 2 >= ar_3 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwise1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise2(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwise0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise1(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise0(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb0in(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
4.88/2.31	
4.88/2.31		start location:	koat_start
4.88/2.31	
4.88/2.31		leaf cost:	0
4.88/2.31	
4.88/2.31	
4.88/2.31	
4.88/2.31	Repeatedly propagating knowledge in problem 2 produces the following problem:
4.88/2.31	
4.88/2.31	3:	T:
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\ ar_2 + 2 >= ar_3 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)    evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)    evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)    evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)    evalwise1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise2(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)    evalwise0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise1(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)    evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise0(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)    evalwisestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb0in(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
4.88/2.31	
4.88/2.31		start location:	koat_start
4.88/2.31	
4.88/2.31		leaf cost:	0
4.88/2.31	
4.88/2.31	
4.88/2.31	
4.88/2.31	A polynomial rank function with
4.88/2.31	
4.88/2.31		Pol(evalwisecritedgein) = 2
4.88/2.31	
4.88/2.31		Pol(evalwisebb1in) = 2
4.88/2.31	
4.88/2.31		Pol(evalwisebb2in) = 1
4.88/2.31	
4.88/2.31		Pol(evalwisestop) = 0
4.88/2.31	
4.88/2.31		Pol(evalwise2) = 2
4.88/2.31	
4.88/2.31		Pol(evalwise1) = 2
4.88/2.31	
4.88/2.31		Pol(evalwise0) = 2
4.88/2.31	
4.88/2.31		Pol(evalwisebb0in) = 2
4.88/2.31	
4.88/2.31		Pol(evalwisestart) = 2
4.88/2.31	
4.88/2.31		Pol(koat_start) = 2
4.88/2.31	
4.88/2.31	orients all transitions weakly and the transitions
4.88/2.31	
4.88/2.31		evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31		evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\ ar_2 + 2 >= ar_3 ]
4.88/2.31	
4.88/2.31	strictly and produces the following problem:
4.88/2.31	
4.88/2.31	4:	T:
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]
4.88/2.31	
4.88/2.31			(Comp: 2, Cost: 1)    evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\ ar_2 + 2 >= ar_3 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)    evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]
4.88/2.31	
4.88/2.31			(Comp: 2, Cost: 1)    evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)    evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)    evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)    evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)    evalwise1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise2(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)    evalwise0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise1(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)    evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise0(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)    evalwisestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb0in(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
4.88/2.31	
4.88/2.31		start location:	koat_start
4.88/2.31	
4.88/2.31		leaf cost:	0
4.88/2.31	
4.88/2.31	
4.88/2.31	
4.88/2.31	A polynomial rank function with
4.88/2.31	
4.88/2.31		Pol(evalwisebb1in) = -2*V_3 + 2*V_4 + 1
4.88/2.31	
4.88/2.31		Pol(evalwisecritedgein) = -2*V_3 + 2*V_4
4.88/2.31	
4.88/2.31	and size complexities
4.88/2.31	
4.88/2.31		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
4.88/2.31	
4.88/2.31		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
4.88/2.31	
4.88/2.31		S("evalwisestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwisestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwisestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
4.88/2.31	
4.88/2.31		S("evalwisestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
4.88/2.31	
4.88/2.31		S("evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise0(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise0(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise0(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
4.88/2.31	
4.88/2.31		S("evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise0(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
4.88/2.31	
4.88/2.31		S("evalwise0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise1(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwise0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise1(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwise0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise1(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
4.88/2.31	
4.88/2.31		S("evalwise0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise1(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
4.88/2.31	
4.88/2.31		S("evalwise1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise2(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwise1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise2(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwise1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise2(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
4.88/2.31	
4.88/2.31		S("evalwise1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise2(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-2) = ar_2
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-3) = ar_3
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]", 0-2) = ar_2
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]", 0-3) = ar_3
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-2) = ar_0
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-3) = ar_1
4.88/2.31	
4.88/2.31		S("evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
4.88/2.31	
4.88/2.31		S("evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
4.88/2.31	
4.88/2.31		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]", 0-2) = ar_0
4.88/2.31	
4.88/2.31		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]", 0-3) = ?
4.88/2.31	
4.88/2.31		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]", 0-2) = ?
4.88/2.31	
4.88/2.31		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]", 0-3) = ar_1
4.88/2.31	
4.88/2.31		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\\ ar_2 + 2 >= ar_3 ]", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\\ ar_2 + 2 >= ar_3 ]", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\\ ar_2 + 2 >= ar_3 ]", 0-2) = ?
4.88/2.31	
4.88/2.31		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\\ ar_2 + 2 >= ar_3 ]", 0-3) = ?
4.88/2.31	
4.88/2.31		S("evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]", 0-2) = ar_0
4.88/2.31	
4.88/2.31		S("evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]", 0-3) = ?
4.88/2.31	
4.88/2.31		S("evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-2) = ?
4.88/2.31	
4.88/2.31		S("evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-3) = ar_1
4.88/2.31	
4.88/2.31	orients the transitions
4.88/2.31	
4.88/2.31		evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]
4.88/2.31	
4.88/2.31		evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]
4.88/2.31	
4.88/2.31	weakly and the transitions
4.88/2.31	
4.88/2.31		evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]
4.88/2.31	
4.88/2.31		evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]
4.88/2.31	
4.88/2.31	strictly and produces the following problem:
4.88/2.31	
4.88/2.31	5:	T:
4.88/2.31	
4.88/2.31			(Comp: 2*ar_0 + 2*ar_1 + 1, Cost: 1)    evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)                      evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]
4.88/2.31	
4.88/2.31			(Comp: 2, Cost: 1)                      evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\ ar_2 + 2 >= ar_3 ]
4.88/2.31	
4.88/2.31			(Comp: 2*ar_0 + 2*ar_1 + 1, Cost: 1)    evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]
4.88/2.31	
4.88/2.31			(Comp: ?, Cost: 1)                      evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]
4.88/2.31	
4.88/2.31			(Comp: 2, Cost: 1)                      evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)                      evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)                      evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)                      evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)                      evalwise1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise2(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)                      evalwise0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise1(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)                      evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise0(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 1)                      evalwisestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb0in(ar_0, ar_1, ar_2, ar_3))
4.88/2.31	
4.88/2.31			(Comp: 1, Cost: 0)                      koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
4.88/2.31	
4.88/2.31		start location:	koat_start
4.88/2.31	
4.88/2.31		leaf cost:	0
4.88/2.31	
4.88/2.31	
4.88/2.31	
4.88/2.31	A polynomial rank function with
4.88/2.31	
4.88/2.31		Pol(evalwisecritedgein) = 2*V_3 - 2*V_4 + 1
4.88/2.31	
4.88/2.31		Pol(evalwisebb1in) = 2*V_3 - 2*V_4 + 2
4.88/2.31	
4.88/2.31	and size complexities
4.88/2.31	
4.88/2.31		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
4.88/2.31	
4.88/2.31		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
4.88/2.31	
4.88/2.31		S("evalwisestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwisestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwisestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
4.88/2.31	
4.88/2.31		S("evalwisestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
4.88/2.31	
4.88/2.31		S("evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise0(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise0(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise0(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
4.88/2.31	
4.88/2.31		S("evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise0(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
4.88/2.31	
4.88/2.31		S("evalwise0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise1(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwise0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise1(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwise0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise1(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
4.88/2.31	
4.88/2.31		S("evalwise0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise1(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
4.88/2.31	
4.88/2.31		S("evalwise1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise2(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwise1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise2(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwise1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise2(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
4.88/2.31	
4.88/2.31		S("evalwise1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise2(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-2) = ar_2
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-3) = ar_3
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]", 0-1) = ar_1
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]", 0-2) = ar_2
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]", 0-3) = ar_3
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-0) = ar_0
4.88/2.31	
4.88/2.31		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-1) = ar_1
4.88/2.32	
4.88/2.32		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-2) = ar_0
4.88/2.32	
4.88/2.32		S("evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-3) = ar_1
4.88/2.32	
4.88/2.32		S("evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
4.88/2.32	
4.88/2.32		S("evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
4.88/2.32	
4.88/2.32		S("evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3))", 0-2) = 3*ar_0 + 3*ar_1 + 3*ar_2 + 81
4.88/2.32	
4.88/2.32		S("evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
4.88/2.32	
4.88/2.32		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]", 0-0) = ar_0
4.88/2.32	
4.88/2.32		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]", 0-1) = ar_1
4.88/2.32	
4.88/2.32		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]", 0-2) = ar_0
4.88/2.32	
4.88/2.32		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]", 0-3) = ?
4.88/2.32	
4.88/2.32		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]", 0-0) = ar_0
4.88/2.32	
4.88/2.32		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]", 0-1) = ar_1
4.88/2.32	
4.88/2.32		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]", 0-2) = 3*ar_0 + 3*ar_1 + 9
4.88/2.32	
4.88/2.32		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]", 0-3) = ar_1
4.88/2.32	
4.88/2.32		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\\ ar_2 + 2 >= ar_3 ]", 0-0) = ar_0
4.88/2.32	
4.88/2.32		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\\ ar_2 + 2 >= ar_3 ]", 0-1) = ar_1
4.88/2.32	
4.88/2.32		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\\ ar_2 + 2 >= ar_3 ]", 0-2) = 3*ar_0 + 3*ar_1 + 27
4.88/2.32	
4.88/2.32		S("evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\\ ar_2 + 2 >= ar_3 ]", 0-3) = ?
4.88/2.32	
4.88/2.32		S("evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]", 0-0) = ar_0
4.88/2.32	
4.88/2.32		S("evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]", 0-1) = ar_1
4.88/2.32	
4.88/2.32		S("evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]", 0-2) = ar_0
4.88/2.32	
4.88/2.32		S("evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]", 0-3) = ?
4.88/2.32	
4.88/2.32		S("evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-0) = ar_0
4.88/2.32	
4.88/2.32		S("evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-1) = ar_1
4.88/2.32	
4.88/2.32		S("evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-2) = 3*ar_0 + 3*ar_1 + 9
4.88/2.32	
4.88/2.32		S("evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-3) = ar_1
4.88/2.32	
4.88/2.32	orients the transitions
4.88/2.32	
4.88/2.32		evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]
4.88/2.32	
4.88/2.32		evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]
4.88/2.32	
4.88/2.32	weakly and the transitions
4.88/2.32	
4.88/2.32		evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]
4.88/2.32	
4.88/2.32		evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]
4.88/2.32	
4.88/2.32	strictly and produces the following problem:
4.88/2.32	
4.88/2.32	6:	T:
4.88/2.32	
4.88/2.32			(Comp: 2*ar_0 + 2*ar_1 + 1, Cost: 1)    evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ]
4.88/2.32	
4.88/2.32			(Comp: 2*ar_0 + 2*ar_1 + 2, Cost: 1)    evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ]
4.88/2.32	
4.88/2.32			(Comp: 2, Cost: 1)                      evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\ ar_2 + 2 >= ar_3 ]
4.88/2.32	
4.88/2.32			(Comp: 2*ar_0 + 2*ar_1 + 1, Cost: 1)    evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ]
4.88/2.32	
4.88/2.32			(Comp: 2*ar_0 + 2*ar_1 + 2, Cost: 1)    evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ]
4.88/2.32	
4.88/2.32			(Comp: 2, Cost: 1)                      evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3))
4.88/2.32	
4.88/2.32			(Comp: 1, Cost: 1)                      evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
4.88/2.32	
4.88/2.32			(Comp: 1, Cost: 1)                      evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ]
4.88/2.32	
4.88/2.32			(Comp: 1, Cost: 1)                      evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
4.88/2.32	
4.88/2.32			(Comp: 1, Cost: 1)                      evalwise1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise2(ar_0, ar_1, ar_2, ar_3))
4.88/2.32	
4.88/2.32			(Comp: 1, Cost: 1)                      evalwise0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise1(ar_0, ar_1, ar_2, ar_3))
4.88/2.32	
4.88/2.32			(Comp: 1, Cost: 1)                      evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise0(ar_0, ar_1, ar_2, ar_3))
4.88/2.32	
4.88/2.32			(Comp: 1, Cost: 1)                      evalwisestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb0in(ar_0, ar_1, ar_2, ar_3))
4.88/2.32	
4.88/2.32			(Comp: 1, Cost: 0)                      koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
4.88/2.32	
4.88/2.32		start location:	koat_start
4.88/2.32	
4.88/2.32		leaf cost:	0
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	Complexity upper bound 8*ar_0 + 8*ar_1 + 17
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	Time: 0.167 sec (SMT: 0.131 sec)
4.88/2.32	
4.88/2.32	
4.88/2.32	----------------------------------------
4.88/2.32	
4.88/2.32	(2)
4.88/2.32	BOUNDS(1, n^1)
4.88/2.32	
4.88/2.32	----------------------------------------
4.88/2.32	
4.88/2.32	(3) Loat Proof (FINISHED)
4.88/2.32	
4.88/2.32	
4.88/2.32	### Pre-processing the ITS problem ###
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	Initial linear ITS problem
4.88/2.32	
4.88/2.32	   Start location: evalwisestart
4.88/2.32	
4.88/2.32	      0: evalwisestart -> evalwisebb0in : [], cost: 1
4.88/2.32	
4.88/2.32	      1: evalwisebb0in -> evalwise0 : [], cost: 1
4.88/2.32	
4.88/2.32	      2: evalwise0 -> evalwise1 : [], cost: 1
4.88/2.32	
4.88/2.32	      3: evalwise1 -> evalwise2 : [], cost: 1
4.88/2.32	
4.88/2.32	      4: evalwise2 -> evalwisebb2in : [ 0>=1+A ], cost: 1
4.88/2.32	
4.88/2.32	      5: evalwise2 -> evalwisebb2in : [ 0>=1+B ], cost: 1
4.88/2.32	
4.88/2.32	      6: evalwise2 -> evalwisebb1in : C'=A, D'=B, [ A>=0 && B>=0 ], cost: 1
4.88/2.32	
4.88/2.32	      7: evalwisebb1in -> evalwisecritedgein : [ C>=3+D ], cost: 1
4.88/2.32	
4.88/2.32	      8: evalwisebb1in -> evalwisecritedgein : [ D>=3+C ], cost: 1
4.88/2.32	
4.88/2.32	      9: evalwisebb1in -> evalwisebb2in : [ 2+D>=C && 2+C>=D ], cost: 1
4.88/2.32	
4.88/2.32	     10: evalwisecritedgein -> evalwisebb1in : C'=1+C, [ D>=1+C ], cost: 1
4.88/2.32	
4.88/2.32	     11: evalwisecritedgein -> evalwisebb1in : [ D>=1+C && C>=D ], cost: 1
4.88/2.32	
4.88/2.32	     12: evalwisecritedgein -> evalwisebb1in : C'=1+C, D'=1+D, [ C>=D && D>=1+C ], cost: 1
4.88/2.32	
4.88/2.32	     13: evalwisecritedgein -> evalwisebb1in : D'=1+D, [ C>=D ], cost: 1
4.88/2.32	
4.88/2.32	     14: evalwisebb2in -> evalwisestop : [], cost: 1
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	Removed unreachable and leaf rules:
4.88/2.32	
4.88/2.32	   Start location: evalwisestart
4.88/2.32	
4.88/2.32	      0: evalwisestart -> evalwisebb0in : [], cost: 1
4.88/2.32	
4.88/2.32	      1: evalwisebb0in -> evalwise0 : [], cost: 1
4.88/2.32	
4.88/2.32	      2: evalwise0 -> evalwise1 : [], cost: 1
4.88/2.32	
4.88/2.32	      3: evalwise1 -> evalwise2 : [], cost: 1
4.88/2.32	
4.88/2.32	      6: evalwise2 -> evalwisebb1in : C'=A, D'=B, [ A>=0 && B>=0 ], cost: 1
4.88/2.32	
4.88/2.32	      7: evalwisebb1in -> evalwisecritedgein : [ C>=3+D ], cost: 1
4.88/2.32	
4.88/2.32	      8: evalwisebb1in -> evalwisecritedgein : [ D>=3+C ], cost: 1
4.88/2.32	
4.88/2.32	     10: evalwisecritedgein -> evalwisebb1in : C'=1+C, [ D>=1+C ], cost: 1
4.88/2.32	
4.88/2.32	     11: evalwisecritedgein -> evalwisebb1in : [ D>=1+C && C>=D ], cost: 1
4.88/2.32	
4.88/2.32	     12: evalwisecritedgein -> evalwisebb1in : C'=1+C, D'=1+D, [ C>=D && D>=1+C ], cost: 1
4.88/2.32	
4.88/2.32	     13: evalwisecritedgein -> evalwisebb1in : D'=1+D, [ C>=D ], cost: 1
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	Removed rules with unsatisfiable guard:
4.88/2.32	
4.88/2.32	   Start location: evalwisestart
4.88/2.32	
4.88/2.32	      0: evalwisestart -> evalwisebb0in : [], cost: 1
4.88/2.32	
4.88/2.32	      1: evalwisebb0in -> evalwise0 : [], cost: 1
4.88/2.32	
4.88/2.32	      2: evalwise0 -> evalwise1 : [], cost: 1
4.88/2.32	
4.88/2.32	      3: evalwise1 -> evalwise2 : [], cost: 1
4.88/2.32	
4.88/2.32	      6: evalwise2 -> evalwisebb1in : C'=A, D'=B, [ A>=0 && B>=0 ], cost: 1
4.88/2.32	
4.88/2.32	      7: evalwisebb1in -> evalwisecritedgein : [ C>=3+D ], cost: 1
4.88/2.32	
4.88/2.32	      8: evalwisebb1in -> evalwisecritedgein : [ D>=3+C ], cost: 1
4.88/2.32	
4.88/2.32	     10: evalwisecritedgein -> evalwisebb1in : C'=1+C, [ D>=1+C ], cost: 1
4.88/2.32	
4.88/2.32	     13: evalwisecritedgein -> evalwisebb1in : D'=1+D, [ C>=D ], cost: 1
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	### Simplification by acceleration and chaining ###
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	Eliminated locations (on linear paths):
4.88/2.32	
4.88/2.32	   Start location: evalwisestart
4.88/2.32	
4.88/2.32	     18: evalwisestart -> evalwisebb1in : C'=A, D'=B, [ A>=0 && B>=0 ], cost: 5
4.88/2.32	
4.88/2.32	      7: evalwisebb1in -> evalwisecritedgein : [ C>=3+D ], cost: 1
4.88/2.32	
4.88/2.32	      8: evalwisebb1in -> evalwisecritedgein : [ D>=3+C ], cost: 1
4.88/2.32	
4.88/2.32	     10: evalwisecritedgein -> evalwisebb1in : C'=1+C, [ D>=1+C ], cost: 1
4.88/2.32	
4.88/2.32	     13: evalwisecritedgein -> evalwisebb1in : D'=1+D, [ C>=D ], cost: 1
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	Eliminated locations (on tree-shaped paths):
4.88/2.32	
4.88/2.32	   Start location: evalwisestart
4.88/2.32	
4.88/2.32	     18: evalwisestart -> evalwisebb1in : C'=A, D'=B, [ A>=0 && B>=0 ], cost: 5
4.88/2.32	
4.88/2.32	     19: evalwisebb1in -> evalwisebb1in : D'=1+D, [ C>=3+D ], cost: 2
4.88/2.32	
4.88/2.32	     20: evalwisebb1in -> evalwisebb1in : C'=1+C, [ D>=3+C ], cost: 2
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	Accelerating simple loops of location 5.
4.88/2.32	
4.88/2.32	   Accelerating the following rules:
4.88/2.32	
4.88/2.32	     19: evalwisebb1in -> evalwisebb1in : D'=1+D, [ C>=3+D ], cost: 2
4.88/2.32	
4.88/2.32	     20: evalwisebb1in -> evalwisebb1in : C'=1+C, [ D>=3+C ], cost: 2
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	   Accelerated rule 19 with metering function -2+C-D, yielding the new rule 21.
4.88/2.32	
4.88/2.32	   Accelerated rule 20 with metering function -2-C+D, yielding the new rule 22.
4.88/2.32	
4.88/2.32	   Removing the simple loops: 19 20.
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	Accelerated all simple loops using metering functions (where possible):
4.88/2.32	
4.88/2.32	   Start location: evalwisestart
4.88/2.32	
4.88/2.32	     18: evalwisestart -> evalwisebb1in : C'=A, D'=B, [ A>=0 && B>=0 ], cost: 5
4.88/2.32	
4.88/2.32	     21: evalwisebb1in -> evalwisebb1in : D'=-2+C, [ C>=3+D ], cost: -4+2*C-2*D
4.88/2.32	
4.88/2.32	     22: evalwisebb1in -> evalwisebb1in : C'=-2+D, [ D>=3+C ], cost: -4-2*C+2*D
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	Chained accelerated rules (with incoming rules):
4.88/2.32	
4.88/2.32	   Start location: evalwisestart
4.88/2.32	
4.88/2.32	     18: evalwisestart -> evalwisebb1in : C'=A, D'=B, [ A>=0 && B>=0 ], cost: 5
4.88/2.32	
4.88/2.32	     23: evalwisestart -> evalwisebb1in : C'=A, D'=-2+A, [ A>=0 && B>=0 && A>=3+B ], cost: 1+2*A-2*B
4.88/2.32	
4.88/2.32	     24: evalwisestart -> evalwisebb1in : C'=-2+B, D'=B, [ A>=0 && B>=0 && B>=3+A ], cost: 1-2*A+2*B
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	Removed unreachable locations (and leaf rules with constant cost):
4.88/2.32	
4.88/2.32	   Start location: evalwisestart
4.88/2.32	
4.88/2.32	     23: evalwisestart -> evalwisebb1in : C'=A, D'=-2+A, [ A>=0 && B>=0 && A>=3+B ], cost: 1+2*A-2*B
4.88/2.32	
4.88/2.32	     24: evalwisestart -> evalwisebb1in : C'=-2+B, D'=B, [ A>=0 && B>=0 && B>=3+A ], cost: 1-2*A+2*B
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	### Computing asymptotic complexity ###
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	Fully simplified ITS problem
4.88/2.32	
4.88/2.32	   Start location: evalwisestart
4.88/2.32	
4.88/2.32	     23: evalwisestart -> evalwisebb1in : C'=A, D'=-2+A, [ A>=0 && B>=0 && A>=3+B ], cost: 1+2*A-2*B
4.88/2.32	
4.88/2.32	     24: evalwisestart -> evalwisebb1in : C'=-2+B, D'=B, [ A>=0 && B>=0 && B>=3+A ], cost: 1-2*A+2*B
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	Computing asymptotic complexity for rule 23
4.88/2.32	
4.88/2.32	   Simplified the guard:
4.88/2.32	
4.88/2.32	     23: evalwisestart -> evalwisebb1in : C'=A, D'=-2+A, [ B>=0 && A>=3+B ], cost: 1+2*A-2*B
4.88/2.32	
4.88/2.32	   Solved the limit problem by the following transformations:
4.88/2.32	
4.88/2.32	      Created initial limit problem:
4.88/2.32	
4.88/2.32	      1+B (+/+!), -2+A-B (+/+!), 1+2*A-2*B (+) [not solved]
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	      applying transformation rule (C) using substitution {B==0}
4.88/2.32	
4.88/2.32	      resulting limit problem:
4.88/2.32	
4.88/2.32	      1 (+/+!), 1+2*A (+), -2+A (+/+!) [not solved]
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	      applying transformation rule (C) using substitution {A==3+B}
4.88/2.32	
4.88/2.32	      resulting limit problem:
4.88/2.32	
4.88/2.32	      1 (+/+!), 1+B (+/+!), 7+2*B (+) [not solved]
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	      applying transformation rule (B), deleting 1 (+/+!)
4.88/2.32	
4.88/2.32	      resulting limit problem:
4.88/2.32	
4.88/2.32	      1+B (+/+!), 7+2*B (+) [not solved]
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	      applying transformation rule (D), replacing 1+B (+/+!) by B (+)
4.88/2.32	
4.88/2.32	      resulting limit problem:
4.88/2.32	
4.88/2.32	      7+2*B (+), B (+) [not solved]
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	      applying transformation rule (D), replacing 7+2*B (+) by 2*B (+)
4.88/2.32	
4.88/2.32	      resulting limit problem:
4.88/2.32	
4.88/2.32	      2*B (+), B (+) [not solved]
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	      applying transformation rule (A), replacing 2*B (+) by B (+) and 2 (+!) using + limit vector (+,+!)
4.88/2.32	
4.88/2.32	      resulting limit problem:
4.88/2.32	
4.88/2.32	      2 (+!), B (+) [not solved]
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	      applying transformation rule (B), deleting 2 (+!)
4.88/2.32	
4.88/2.32	      resulting limit problem:
4.88/2.32	
4.88/2.32	      B (+) [solved]
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	   Solution:
4.88/2.32	
4.88/2.32	      A / 3+n
4.88/2.32	
4.88/2.32	      B / 0
4.88/2.32	
4.88/2.32	   Resulting cost 7+2*n has complexity: Poly(n^1)
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	Found new complexity Poly(n^1).
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	Obtained the following overall complexity (w.r.t. the length of the input n):
4.88/2.32	
4.88/2.32	   Complexity:  Poly(n^1)
4.88/2.32	
4.88/2.32	   Cpx degree:  1
4.88/2.32	
4.88/2.32	   Solved cost: 7+2*n
4.88/2.32	
4.88/2.32	   Rule cost:   1+2*A-2*B
4.88/2.32	
4.88/2.32	   Rule guard:  [ B>=0 && A>=3+B ]
4.88/2.32	
4.88/2.32	
4.88/2.32	
4.88/2.32	WORST_CASE(Omega(n^1),?)
4.88/2.32	
4.88/2.32	
4.88/2.32	----------------------------------------
4.88/2.32	
4.88/2.32	(4)
4.88/2.32	BOUNDS(n^1, INF)
4.88/2.33	EOF