5.19/3.15	WORST_CASE(Omega(n^1), O(n^1))
5.19/3.16	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.19/3.16	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.19/3.16	
5.19/3.16	
5.19/3.16	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
5.19/3.16	
5.19/3.16	(0) CpxIntTrs
5.19/3.16	(1) Koat Proof [FINISHED, 113 ms]
5.19/3.16	(2) BOUNDS(1, n^1)
5.19/3.16	(3) Loat Proof [FINISHED, 728 ms]
5.19/3.16	(4) BOUNDS(n^1, INF)
5.19/3.16	
5.19/3.16	
5.19/3.16	----------------------------------------
5.19/3.16	
5.19/3.16	(0)
5.19/3.16	Obligation:
5.19/3.16	Complexity Int TRS consisting of the following rules:
5.19/3.16	eval_wcet2_start(v__0, v_4, v_i, v_j_0) -> Com_1(eval_wcet2_bb0_in(v__0, v_4, v_i, v_j_0)) :|: TRUE
5.19/3.16	eval_wcet2_bb0_in(v__0, v_4, v_i, v_j_0) -> Com_1(eval_wcet2_0(v__0, v_4, v_i, v_j_0)) :|: TRUE
5.19/3.16	eval_wcet2_0(v__0, v_4, v_i, v_j_0) -> Com_1(eval_wcet2_1(v__0, v_4, v_i, v_j_0)) :|: TRUE
5.19/3.16	eval_wcet2_1(v__0, v_4, v_i, v_j_0) -> Com_1(eval_wcet2_2(v__0, v_4, v_i, v_j_0)) :|: TRUE
5.19/3.16	eval_wcet2_2(v__0, v_4, v_i, v_j_0) -> Com_1(eval_wcet2_3(v__0, v_4, v_i, v_j_0)) :|: TRUE
5.19/3.16	eval_wcet2_3(v__0, v_4, v_i, v_j_0) -> Com_1(eval_wcet2_bb1_in(v_i, v_4, v_i, v_j_0)) :|: TRUE
5.19/3.16	eval_wcet2_bb1_in(v__0, v_4, v_i, v_j_0) -> Com_1(eval_wcet2_bb2_in(v__0, v_4, v_i, 0)) :|: v__0 < 5
5.19/3.16	eval_wcet2_bb1_in(v__0, v_4, v_i, v_j_0) -> Com_1(eval_wcet2_bb5_in(v__0, v_4, v_i, v_j_0)) :|: v__0 >= 5
5.19/3.16	eval_wcet2_bb2_in(v__0, v_4, v_i, v_j_0) -> Com_1(eval_wcet2_bb3_in(v__0, v_4, v_i, v_j_0)) :|: v__0 > 2 && v_j_0 <= 9
5.19/3.16	eval_wcet2_bb2_in(v__0, v_4, v_i, v_j_0) -> Com_1(eval_wcet2_bb4_in(v__0, v_4, v_i, v_j_0)) :|: v__0 <= 2
5.19/3.16	eval_wcet2_bb2_in(v__0, v_4, v_i, v_j_0) -> Com_1(eval_wcet2_bb4_in(v__0, v_4, v_i, v_j_0)) :|: v_j_0 > 9
5.19/3.16	eval_wcet2_bb3_in(v__0, v_4, v_i, v_j_0) -> Com_1(eval_wcet2_bb2_in(v__0, v_4, v_i, v_j_0 + 1)) :|: TRUE
5.19/3.16	eval_wcet2_bb4_in(v__0, v_4, v_i, v_j_0) -> Com_1(eval_wcet2_7(v__0, v__0 + 1, v_i, v_j_0)) :|: TRUE
5.19/3.16	eval_wcet2_7(v__0, v_4, v_i, v_j_0) -> Com_1(eval_wcet2_8(v__0, v_4, v_i, v_j_0)) :|: TRUE
5.19/3.16	eval_wcet2_8(v__0, v_4, v_i, v_j_0) -> Com_1(eval_wcet2_bb1_in(v_4, v_4, v_i, v_j_0)) :|: TRUE
5.19/3.16	eval_wcet2_bb5_in(v__0, v_4, v_i, v_j_0) -> Com_1(eval_wcet2_stop(v__0, v_4, v_i, v_j_0)) :|: TRUE
5.19/3.16	
5.19/3.16	The start-symbols are:[eval_wcet2_start_4]
5.19/3.16	
5.19/3.16	
5.19/3.16	----------------------------------------
5.19/3.16	
5.19/3.16	(1) Koat Proof (FINISHED)
5.19/3.16	YES(?, 100*ar_1 + 460)
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Initial complexity problem:
5.19/3.16	
5.19/3.16	1:	T:
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet20(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet21(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet22(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet23(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0, ar_3)) [ 4 >= ar_0 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 5 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 10 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet27(ar_0, ar_1, ar_2, ar_0 + 1))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet27(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet28(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_3, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.19/3.16	
5.19/3.16		start location:	koat_start
5.19/3.16	
5.19/3.16		leaf cost:	0
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Repeatedly propagating knowledge in problem 1 produces the following problem:
5.19/3.16	
5.19/3.16	2:	T:
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)    evalwcet2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)    evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet20(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)    evalwcet20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet21(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)    evalwcet21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet22(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)    evalwcet22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet23(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)    evalwcet23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0, ar_3)) [ 4 >= ar_0 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 5 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 10 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet27(ar_0, ar_1, ar_2, ar_0 + 1))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet27(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet28(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_3, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.19/3.16	
5.19/3.16		start location:	koat_start
5.19/3.16	
5.19/3.16		leaf cost:	0
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	A polynomial rank function with
5.19/3.16	
5.19/3.16		Pol(evalwcet2start) = 2
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb0in) = 2
5.19/3.16	
5.19/3.16		Pol(evalwcet20) = 2
5.19/3.16	
5.19/3.16		Pol(evalwcet21) = 2
5.19/3.16	
5.19/3.16		Pol(evalwcet22) = 2
5.19/3.16	
5.19/3.16		Pol(evalwcet23) = 2
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb1in) = 2
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb2in) = 2
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb5in) = 1
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb3in) = 2
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb4in) = 2
5.19/3.16	
5.19/3.16		Pol(evalwcet27) = 2
5.19/3.16	
5.19/3.16		Pol(evalwcet28) = 2
5.19/3.16	
5.19/3.16		Pol(evalwcet2stop) = 0
5.19/3.16	
5.19/3.16		Pol(koat_start) = 2
5.19/3.16	
5.19/3.16	orients all transitions weakly and the transitions
5.19/3.16	
5.19/3.16		evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16		evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 5 ]
5.19/3.16	
5.19/3.16	strictly and produces the following problem:
5.19/3.16	
5.19/3.16	3:	T:
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)    evalwcet2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)    evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet20(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)    evalwcet20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet21(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)    evalwcet21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet22(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)    evalwcet22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet23(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)    evalwcet23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0, ar_3)) [ 4 >= ar_0 ]
5.19/3.16	
5.19/3.16			(Comp: 2, Cost: 1)    evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 5 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 10 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet27(ar_0, ar_1, ar_2, ar_0 + 1))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet27(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet28(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)    evalwcet28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_3, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 2, Cost: 1)    evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.19/3.16	
5.19/3.16		start location:	koat_start
5.19/3.16	
5.19/3.16		leaf cost:	0
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	A polynomial rank function with
5.19/3.16	
5.19/3.16		Pol(evalwcet2start) = -2*V_2 + 9
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb0in) = -2*V_2 + 9
5.19/3.16	
5.19/3.16		Pol(evalwcet20) = -2*V_2 + 9
5.19/3.16	
5.19/3.16		Pol(evalwcet21) = -2*V_2 + 9
5.19/3.16	
5.19/3.16		Pol(evalwcet22) = -2*V_2 + 9
5.19/3.16	
5.19/3.16		Pol(evalwcet23) = -2*V_2 + 9
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb1in) = -2*V_1 + 9
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb2in) = -2*V_1 + 8
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb5in) = -2*V_1
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb3in) = -2*V_1 + 8
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb4in) = -2*V_1 + 7
5.19/3.16	
5.19/3.16		Pol(evalwcet27) = -2*V_4 + 9
5.19/3.16	
5.19/3.16		Pol(evalwcet28) = -2*V_4 + 9
5.19/3.16	
5.19/3.16		Pol(evalwcet2stop) = -2*V_1
5.19/3.16	
5.19/3.16		Pol(koat_start) = -2*V_2 + 9
5.19/3.16	
5.19/3.16	orients all transitions weakly and the transitions
5.19/3.16	
5.19/3.16		evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]
5.19/3.16	
5.19/3.16		evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0, ar_3)) [ 4 >= ar_0 ]
5.19/3.16	
5.19/3.16	strictly and produces the following problem:
5.19/3.16	
5.19/3.16	4:	T:
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)             evalwcet2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)             evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet20(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)             evalwcet20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet21(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)             evalwcet21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet22(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)             evalwcet22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet23(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)             evalwcet23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 2*ar_1 + 9, Cost: 1)    evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0, ar_3)) [ 4 >= ar_0 ]
5.19/3.16	
5.19/3.16			(Comp: 2, Cost: 1)             evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 5 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)             evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
5.19/3.16	
5.19/3.16			(Comp: 2*ar_1 + 9, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)             evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 10 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)             evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)             evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet27(ar_0, ar_1, ar_2, ar_0 + 1))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)             evalwcet27(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet28(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)             evalwcet28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_3, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 2, Cost: 1)             evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.19/3.16	
5.19/3.16		start location:	koat_start
5.19/3.16	
5.19/3.16		leaf cost:	0
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	A polynomial rank function with
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb4in) = 3
5.19/3.16	
5.19/3.16		Pol(evalwcet27) = 2
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb3in) = 4
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb2in) = 4
5.19/3.16	
5.19/3.16		Pol(evalwcet28) = 1
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb1in) = 0
5.19/3.16	
5.19/3.16	and size complexities
5.19/3.16	
5.19/3.16		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
5.19/3.16	
5.19/3.16		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
5.19/3.16	
5.19/3.16		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
5.19/3.16	
5.19/3.16		S("evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
5.19/3.16	
5.19/3.16		S("evalwcet28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-0) = ?
5.19/3.16	
5.19/3.16		S("evalwcet28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-3) = ?
5.19/3.16	
5.19/3.16		S("evalwcet27(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet28(ar_0, ar_1, ar_2, ar_3))", 0-0) = ?
5.19/3.16	
5.19/3.16		S("evalwcet27(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet28(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet27(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet28(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet27(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet28(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet27(ar_0, ar_1, ar_2, ar_0 + 1))", 0-0) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet27(ar_0, ar_1, ar_2, ar_0 + 1))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet27(ar_0, ar_1, ar_2, ar_0 + 1))", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet27(ar_0, ar_1, ar_2, ar_0 + 1))", 0-3) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-0) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-3) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 10 ]", 0-0) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 10 ]", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 10 ]", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 10 ]", 0-3) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-0) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-3) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-0) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-3) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 5 ]", 0-0) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 5 ]", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 5 ]", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 5 ]", 0-3) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0, ar_3)) [ 4 >= ar_0 ]", 0-0) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0, ar_3)) [ 4 >= ar_0 ]", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0, ar_3)) [ 4 >= ar_0 ]", 0-2) = 0
5.19/3.16	
5.19/3.16		S("evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0, ar_3)) [ 4 >= ar_0 ]", 0-3) = ?
5.19/3.16	
5.19/3.16		S("evalwcet23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2, ar_3))", 0-0) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.19/3.16	
5.19/3.16		S("evalwcet23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.19/3.16	
5.19/3.16		S("evalwcet22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet23(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.19/3.16	
5.19/3.16		S("evalwcet22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet23(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet23(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.19/3.16	
5.19/3.16		S("evalwcet22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet23(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.19/3.16	
5.19/3.16		S("evalwcet21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet22(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.19/3.16	
5.19/3.16		S("evalwcet21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet22(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet22(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.19/3.16	
5.19/3.16		S("evalwcet21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet22(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.19/3.16	
5.19/3.16		S("evalwcet20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet21(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.19/3.16	
5.19/3.16		S("evalwcet20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet21(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet21(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.19/3.16	
5.19/3.16		S("evalwcet20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet21(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.19/3.16	
5.19/3.16		S("evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet20(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.19/3.16	
5.19/3.16		S("evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet20(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet20(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.19/3.16	
5.19/3.16		S("evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet20(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.19/3.16	
5.19/3.16		S("evalwcet2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.19/3.16	
5.19/3.16		S("evalwcet2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.19/3.16	
5.19/3.16		S("evalwcet2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.19/3.16	
5.19/3.16	orients the transitions
5.19/3.16	
5.19/3.16		evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet27(ar_0, ar_1, ar_2, ar_0 + 1))
5.19/3.16	
5.19/3.16		evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
5.19/3.16	
5.19/3.16		evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 10 ]
5.19/3.16	
5.19/3.16		evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
5.19/3.16	
5.19/3.16		evalwcet28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_3, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16		evalwcet27(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet28(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16	weakly and the transitions
5.19/3.16	
5.19/3.16		evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet27(ar_0, ar_1, ar_2, ar_0 + 1))
5.19/3.16	
5.19/3.16		evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 10 ]
5.19/3.16	
5.19/3.16		evalwcet28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_3, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16		evalwcet27(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet28(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16	strictly and produces the following problem:
5.19/3.16	
5.19/3.16	5:	T:
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet20(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet21(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet22(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet23(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 2*ar_1 + 9, Cost: 1)      evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0, ar_3)) [ 4 >= ar_0 ]
5.19/3.16	
5.19/3.16			(Comp: 2, Cost: 1)               evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 5 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)               evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
5.19/3.16	
5.19/3.16			(Comp: 2*ar_1 + 9, Cost: 1)      evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]
5.19/3.16	
5.19/3.16			(Comp: 14*ar_1 + 63, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 10 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)               evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 14*ar_1 + 63, Cost: 1)    evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet27(ar_0, ar_1, ar_2, ar_0 + 1))
5.19/3.16	
5.19/3.16			(Comp: 14*ar_1 + 63, Cost: 1)    evalwcet27(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet28(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 14*ar_1 + 63, Cost: 1)    evalwcet28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_3, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 2, Cost: 1)               evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 0)               koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.19/3.16	
5.19/3.16		start location:	koat_start
5.19/3.16	
5.19/3.16		leaf cost:	0
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	A polynomial rank function with
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb3in) = -V_3 + 9
5.19/3.16	
5.19/3.16		Pol(evalwcet2bb2in) = -V_3 + 10
5.19/3.16	
5.19/3.16	and size complexities
5.19/3.16	
5.19/3.16		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
5.19/3.16	
5.19/3.16		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
5.19/3.16	
5.19/3.16		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
5.19/3.16	
5.19/3.16		S("evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = 15*ar_1 + 3189375
5.19/3.16	
5.19/3.16		S("evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = 15*ar_1 + 15*ar_3 + 47840625
5.19/3.16	
5.19/3.16		S("evalwcet28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-0) = 15*ar_1 + 14175
5.19/3.16	
5.19/3.16		S("evalwcet28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-3) = 15*ar_1 + 212625
5.19/3.16	
5.19/3.16		S("evalwcet27(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet28(ar_0, ar_1, ar_2, ar_3))", 0-0) = 15*ar_1 + 3189375
5.19/3.16	
5.19/3.16		S("evalwcet27(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet28(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet27(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet28(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet27(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet28(ar_0, ar_1, ar_2, ar_3))", 0-3) = 15*ar_1 + 14175
5.19/3.16	
5.19/3.16		S("evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet27(ar_0, ar_1, ar_2, ar_0 + 1))", 0-0) = 15*ar_1 + 212625
5.19/3.16	
5.19/3.16		S("evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet27(ar_0, ar_1, ar_2, ar_0 + 1))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet27(ar_0, ar_1, ar_2, ar_0 + 1))", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet27(ar_0, ar_1, ar_2, ar_0 + 1))", 0-3) = 15*ar_1 + 14175
5.19/3.16	
5.19/3.16		S("evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-0) = 15*ar_1 + 14175
5.19/3.16	
5.19/3.16		S("evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-3) = 15*ar_1 + 15*ar_3 + 47840625
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 10 ]", 0-0) = 15*ar_1 + 14175
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 10 ]", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 10 ]", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 10 ]", 0-3) = 15*ar_1 + 15*ar_3 + 717609375
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-0) = 15*ar_1 + 14175
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-3) = 15*ar_1 + 15*ar_3 + 717609375
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-0) = 15*ar_1 + 14175
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-3) = 15*ar_1 + 15*ar_3 + 47840625
5.19/3.16	
5.19/3.16		S("evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 5 ]", 0-0) = 15*ar_1 + 212625
5.19/3.16	
5.19/3.16		S("evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 5 ]", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 5 ]", 0-2) = ?
5.19/3.16	
5.19/3.16		S("evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 5 ]", 0-3) = 15*ar_1 + 15*ar_3 + 3189375
5.19/3.16	
5.19/3.16		S("evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0, ar_3)) [ 4 >= ar_0 ]", 0-0) = 15*ar_1 + 14175
5.19/3.16	
5.19/3.16		S("evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0, ar_3)) [ 4 >= ar_0 ]", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0, ar_3)) [ 4 >= ar_0 ]", 0-2) = 0
5.19/3.16	
5.19/3.16		S("evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0, ar_3)) [ 4 >= ar_0 ]", 0-3) = 15*ar_1 + 15*ar_3 + 3189375
5.19/3.16	
5.19/3.16		S("evalwcet23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2, ar_3))", 0-0) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.19/3.16	
5.19/3.16		S("evalwcet23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.19/3.16	
5.19/3.16		S("evalwcet22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet23(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.19/3.16	
5.19/3.16		S("evalwcet22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet23(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet23(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.19/3.16	
5.19/3.16		S("evalwcet22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet23(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.19/3.16	
5.19/3.16		S("evalwcet21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet22(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.19/3.16	
5.19/3.16		S("evalwcet21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet22(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet22(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.19/3.16	
5.19/3.16		S("evalwcet21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet22(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.19/3.16	
5.19/3.16		S("evalwcet20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet21(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.19/3.16	
5.19/3.16		S("evalwcet20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet21(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet21(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.19/3.16	
5.19/3.16		S("evalwcet20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet21(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.19/3.16	
5.19/3.16		S("evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet20(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.19/3.16	
5.19/3.16		S("evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet20(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet20(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.19/3.16	
5.19/3.16		S("evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet20(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.19/3.16	
5.19/3.16		S("evalwcet2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.19/3.16	
5.19/3.16		S("evalwcet2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.19/3.16	
5.19/3.16		S("evalwcet2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.19/3.16	
5.19/3.16		S("evalwcet2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.19/3.16	
5.19/3.16	orients the transitions
5.19/3.16	
5.19/3.16		evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
5.19/3.16	
5.19/3.16		evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
5.19/3.16	
5.19/3.16	weakly and the transition
5.19/3.16	
5.19/3.16		evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
5.19/3.16	
5.19/3.16	strictly and produces the following problem:
5.19/3.16	
5.19/3.16	6:	T:
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet20(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet21(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet22(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet23(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 2*ar_1 + 9, Cost: 1)      evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0, ar_3)) [ 4 >= ar_0 ]
5.19/3.16	
5.19/3.16			(Comp: 2, Cost: 1)               evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 5 ]
5.19/3.16	
5.19/3.16			(Comp: 20*ar_1 + 90, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
5.19/3.16	
5.19/3.16			(Comp: 2*ar_1 + 9, Cost: 1)      evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]
5.19/3.16	
5.19/3.16			(Comp: 14*ar_1 + 63, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 10 ]
5.19/3.16	
5.19/3.16			(Comp: ?, Cost: 1)               evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 14*ar_1 + 63, Cost: 1)    evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet27(ar_0, ar_1, ar_2, ar_0 + 1))
5.19/3.16	
5.19/3.16			(Comp: 14*ar_1 + 63, Cost: 1)    evalwcet27(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet28(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 14*ar_1 + 63, Cost: 1)    evalwcet28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_3, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 2, Cost: 1)               evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 0)               koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.19/3.16	
5.19/3.16		start location:	koat_start
5.19/3.16	
5.19/3.16		leaf cost:	0
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Repeatedly propagating knowledge in problem 6 produces the following problem:
5.19/3.16	
5.19/3.16	7:	T:
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet20(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet21(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet22(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet23(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 1)               evalwcet23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 2*ar_1 + 9, Cost: 1)      evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0, ar_3)) [ 4 >= ar_0 ]
5.19/3.16	
5.19/3.16			(Comp: 2, Cost: 1)               evalwcet2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 5 ]
5.19/3.16	
5.19/3.16			(Comp: 20*ar_1 + 90, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
5.19/3.16	
5.19/3.16			(Comp: 2*ar_1 + 9, Cost: 1)      evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]
5.19/3.16	
5.19/3.16			(Comp: 14*ar_1 + 63, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 10 ]
5.19/3.16	
5.19/3.16			(Comp: 20*ar_1 + 90, Cost: 1)    evalwcet2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 14*ar_1 + 63, Cost: 1)    evalwcet2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet27(ar_0, ar_1, ar_2, ar_0 + 1))
5.19/3.16	
5.19/3.16			(Comp: 14*ar_1 + 63, Cost: 1)    evalwcet27(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet28(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 14*ar_1 + 63, Cost: 1)    evalwcet28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2bb1in(ar_3, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 2, Cost: 1)               evalwcet2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2, ar_3))
5.19/3.16	
5.19/3.16			(Comp: 1, Cost: 0)               koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.19/3.16	
5.19/3.16		start location:	koat_start
5.19/3.16	
5.19/3.16		leaf cost:	0
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Complexity upper bound 100*ar_1 + 460
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Time: 0.183 sec (SMT: 0.140 sec)
5.19/3.16	
5.19/3.16	
5.19/3.16	----------------------------------------
5.19/3.16	
5.19/3.16	(2)
5.19/3.16	BOUNDS(1, n^1)
5.19/3.16	
5.19/3.16	----------------------------------------
5.19/3.16	
5.19/3.16	(3) Loat Proof (FINISHED)
5.19/3.16	
5.19/3.16	
5.19/3.16	### Pre-processing the ITS problem ###
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Initial linear ITS problem
5.19/3.16	
5.19/3.16	   Start location: evalwcet2start
5.19/3.16	
5.19/3.16	      0: evalwcet2start -> evalwcet2bb0in : [], cost: 1
5.19/3.16	
5.19/3.16	      1: evalwcet2bb0in -> evalwcet20 : [], cost: 1
5.19/3.16	
5.19/3.16	      2: evalwcet20 -> evalwcet21 : [], cost: 1
5.19/3.16	
5.19/3.16	      3: evalwcet21 -> evalwcet22 : [], cost: 1
5.19/3.16	
5.19/3.16	      4: evalwcet22 -> evalwcet23 : [], cost: 1
5.19/3.16	
5.19/3.16	      5: evalwcet23 -> evalwcet2bb1in : A'=B, [], cost: 1
5.19/3.16	
5.19/3.16	      6: evalwcet2bb1in -> evalwcet2bb2in : C'=0, [ 4>=A ], cost: 1
5.19/3.16	
5.19/3.16	      7: evalwcet2bb1in -> evalwcet2bb5in : [ A>=5 ], cost: 1
5.19/3.16	
5.19/3.16	      8: evalwcet2bb2in -> evalwcet2bb3in : [ A>=3 && 9>=C ], cost: 1
5.19/3.16	
5.19/3.16	      9: evalwcet2bb2in -> evalwcet2bb4in : [ 2>=A ], cost: 1
5.19/3.16	
5.19/3.16	     10: evalwcet2bb2in -> evalwcet2bb4in : [ C>=10 ], cost: 1
5.19/3.16	
5.19/3.16	     11: evalwcet2bb3in -> evalwcet2bb2in : C'=1+C, [], cost: 1
5.19/3.16	
5.19/3.16	     12: evalwcet2bb4in -> evalwcet27 : D'=1+A, [], cost: 1
5.19/3.16	
5.19/3.16	     13: evalwcet27 -> evalwcet28 : [], cost: 1
5.19/3.16	
5.19/3.16	     14: evalwcet28 -> evalwcet2bb1in : A'=D, [], cost: 1
5.19/3.16	
5.19/3.16	     15: evalwcet2bb5in -> evalwcet2stop : [], cost: 1
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Removed unreachable and leaf rules:
5.19/3.16	
5.19/3.16	   Start location: evalwcet2start
5.19/3.16	
5.19/3.16	      0: evalwcet2start -> evalwcet2bb0in : [], cost: 1
5.19/3.16	
5.19/3.16	      1: evalwcet2bb0in -> evalwcet20 : [], cost: 1
5.19/3.16	
5.19/3.16	      2: evalwcet20 -> evalwcet21 : [], cost: 1
5.19/3.16	
5.19/3.16	      3: evalwcet21 -> evalwcet22 : [], cost: 1
5.19/3.16	
5.19/3.16	      4: evalwcet22 -> evalwcet23 : [], cost: 1
5.19/3.16	
5.19/3.16	      5: evalwcet23 -> evalwcet2bb1in : A'=B, [], cost: 1
5.19/3.16	
5.19/3.16	      6: evalwcet2bb1in -> evalwcet2bb2in : C'=0, [ 4>=A ], cost: 1
5.19/3.16	
5.19/3.16	      8: evalwcet2bb2in -> evalwcet2bb3in : [ A>=3 && 9>=C ], cost: 1
5.19/3.16	
5.19/3.16	      9: evalwcet2bb2in -> evalwcet2bb4in : [ 2>=A ], cost: 1
5.19/3.16	
5.19/3.16	     10: evalwcet2bb2in -> evalwcet2bb4in : [ C>=10 ], cost: 1
5.19/3.16	
5.19/3.16	     11: evalwcet2bb3in -> evalwcet2bb2in : C'=1+C, [], cost: 1
5.19/3.16	
5.19/3.16	     12: evalwcet2bb4in -> evalwcet27 : D'=1+A, [], cost: 1
5.19/3.16	
5.19/3.16	     13: evalwcet27 -> evalwcet28 : [], cost: 1
5.19/3.16	
5.19/3.16	     14: evalwcet28 -> evalwcet2bb1in : A'=D, [], cost: 1
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	### Simplification by acceleration and chaining ###
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Eliminated locations (on linear paths):
5.19/3.16	
5.19/3.16	   Start location: evalwcet2start
5.19/3.16	
5.19/3.16	     20: evalwcet2start -> evalwcet2bb1in : A'=B, [], cost: 6
5.19/3.16	
5.19/3.16	      6: evalwcet2bb1in -> evalwcet2bb2in : C'=0, [ 4>=A ], cost: 1
5.19/3.16	
5.19/3.16	      9: evalwcet2bb2in -> evalwcet2bb4in : [ 2>=A ], cost: 1
5.19/3.16	
5.19/3.16	     10: evalwcet2bb2in -> evalwcet2bb4in : [ C>=10 ], cost: 1
5.19/3.16	
5.19/3.16	     21: evalwcet2bb2in -> evalwcet2bb2in : C'=1+C, [ A>=3 && 9>=C ], cost: 2
5.19/3.16	
5.19/3.16	     23: evalwcet2bb4in -> evalwcet2bb1in : A'=1+A, D'=1+A, [], cost: 3
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Accelerating simple loops of location 7.
5.19/3.16	
5.19/3.16	   Accelerating the following rules:
5.19/3.16	
5.19/3.16	     21: evalwcet2bb2in -> evalwcet2bb2in : C'=1+C, [ A>=3 && 9>=C ], cost: 2
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	   Accelerated rule 21 with metering function 10-C, yielding the new rule 24.
5.19/3.16	
5.19/3.16	   Removing the simple loops: 21.
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Accelerated all simple loops using metering functions (where possible):
5.19/3.16	
5.19/3.16	   Start location: evalwcet2start
5.19/3.16	
5.19/3.16	     20: evalwcet2start -> evalwcet2bb1in : A'=B, [], cost: 6
5.19/3.16	
5.19/3.16	      6: evalwcet2bb1in -> evalwcet2bb2in : C'=0, [ 4>=A ], cost: 1
5.19/3.16	
5.19/3.16	      9: evalwcet2bb2in -> evalwcet2bb4in : [ 2>=A ], cost: 1
5.19/3.16	
5.19/3.16	     10: evalwcet2bb2in -> evalwcet2bb4in : [ C>=10 ], cost: 1
5.19/3.16	
5.19/3.16	     24: evalwcet2bb2in -> evalwcet2bb2in : C'=10, [ A>=3 && 9>=C ], cost: 20-2*C
5.19/3.16	
5.19/3.16	     23: evalwcet2bb4in -> evalwcet2bb1in : A'=1+A, D'=1+A, [], cost: 3
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Chained accelerated rules (with incoming rules):
5.19/3.16	
5.19/3.16	   Start location: evalwcet2start
5.19/3.16	
5.19/3.16	     20: evalwcet2start -> evalwcet2bb1in : A'=B, [], cost: 6
5.19/3.16	
5.19/3.16	      6: evalwcet2bb1in -> evalwcet2bb2in : C'=0, [ 4>=A ], cost: 1
5.19/3.16	
5.19/3.16	     25: evalwcet2bb1in -> evalwcet2bb2in : C'=10, [ 4>=A && A>=3 ], cost: 21
5.19/3.16	
5.19/3.16	      9: evalwcet2bb2in -> evalwcet2bb4in : [ 2>=A ], cost: 1
5.19/3.16	
5.19/3.16	     10: evalwcet2bb2in -> evalwcet2bb4in : [ C>=10 ], cost: 1
5.19/3.16	
5.19/3.16	     23: evalwcet2bb4in -> evalwcet2bb1in : A'=1+A, D'=1+A, [], cost: 3
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Eliminated locations (on tree-shaped paths):
5.19/3.16	
5.19/3.16	   Start location: evalwcet2start
5.19/3.16	
5.19/3.16	     20: evalwcet2start -> evalwcet2bb1in : A'=B, [], cost: 6
5.19/3.16	
5.19/3.16	     26: evalwcet2bb1in -> evalwcet2bb4in : C'=0, [ 2>=A ], cost: 2
5.19/3.16	
5.19/3.16	     27: evalwcet2bb1in -> evalwcet2bb4in : C'=10, [ 4>=A && A>=3 ], cost: 22
5.19/3.16	
5.19/3.16	     23: evalwcet2bb4in -> evalwcet2bb1in : A'=1+A, D'=1+A, [], cost: 3
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Eliminated locations (on tree-shaped paths):
5.19/3.16	
5.19/3.16	   Start location: evalwcet2start
5.19/3.16	
5.19/3.16	     20: evalwcet2start -> evalwcet2bb1in : A'=B, [], cost: 6
5.19/3.16	
5.19/3.16	     28: evalwcet2bb1in -> evalwcet2bb1in : A'=1+A, C'=0, D'=1+A, [ 2>=A ], cost: 5
5.19/3.16	
5.19/3.16	     29: evalwcet2bb1in -> evalwcet2bb1in : A'=1+A, C'=10, D'=1+A, [ 4>=A && A>=3 ], cost: 25
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Accelerating simple loops of location 6.
5.19/3.16	
5.19/3.16	   Accelerating the following rules:
5.19/3.16	
5.19/3.16	     28: evalwcet2bb1in -> evalwcet2bb1in : A'=1+A, C'=0, D'=1+A, [ 2>=A ], cost: 5
5.19/3.16	
5.19/3.16	     29: evalwcet2bb1in -> evalwcet2bb1in : A'=1+A, C'=10, D'=1+A, [ 4>=A && A>=3 ], cost: 25
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	   Accelerated rule 28 with metering function 3-A, yielding the new rule 30.
5.19/3.16	
5.19/3.16	   Accelerated rule 29 with metering function 5-A, yielding the new rule 31.
5.19/3.16	
5.19/3.16	   Removing the simple loops: 28 29.
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Accelerated all simple loops using metering functions (where possible):
5.19/3.16	
5.19/3.16	   Start location: evalwcet2start
5.19/3.16	
5.19/3.16	     20: evalwcet2start -> evalwcet2bb1in : A'=B, [], cost: 6
5.19/3.16	
5.19/3.16	     30: evalwcet2bb1in -> evalwcet2bb1in : A'=3, C'=0, D'=3, [ 2>=A ], cost: 15-5*A
5.19/3.16	
5.19/3.16	     31: evalwcet2bb1in -> evalwcet2bb1in : A'=5, C'=10, D'=5, [ 4>=A && A>=3 ], cost: 125-25*A
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Chained accelerated rules (with incoming rules):
5.19/3.16	
5.19/3.16	   Start location: evalwcet2start
5.19/3.16	
5.19/3.16	     20: evalwcet2start -> evalwcet2bb1in : A'=B, [], cost: 6
5.19/3.16	
5.19/3.16	     32: evalwcet2start -> evalwcet2bb1in : A'=3, C'=0, D'=3, [ 2>=B ], cost: 21-5*B
5.19/3.16	
5.19/3.16	     33: evalwcet2start -> evalwcet2bb1in : A'=5, C'=10, D'=5, [ 4>=B && B>=3 ], cost: 131-25*B
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Removed unreachable locations (and leaf rules with constant cost):
5.19/3.16	
5.19/3.16	   Start location: evalwcet2start
5.19/3.16	
5.19/3.16	     32: evalwcet2start -> evalwcet2bb1in : A'=3, C'=0, D'=3, [ 2>=B ], cost: 21-5*B
5.19/3.16	
5.19/3.16	     33: evalwcet2start -> evalwcet2bb1in : A'=5, C'=10, D'=5, [ 4>=B && B>=3 ], cost: 131-25*B
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	### Computing asymptotic complexity ###
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Fully simplified ITS problem
5.19/3.16	
5.19/3.16	   Start location: evalwcet2start
5.19/3.16	
5.19/3.16	     32: evalwcet2start -> evalwcet2bb1in : A'=3, C'=0, D'=3, [ 2>=B ], cost: 21-5*B
5.19/3.16	
5.19/3.16	     33: evalwcet2start -> evalwcet2bb1in : A'=5, C'=10, D'=5, [ 4>=B && B>=3 ], cost: 131-25*B
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Computing asymptotic complexity for rule 32
5.19/3.16	
5.19/3.16	   Solved the limit problem by the following transformations:
5.19/3.16	
5.19/3.16	      Created initial limit problem:
5.19/3.16	
5.19/3.16	      21-5*B (+), 3-B (+/+!) [not solved]
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	      removing all constraints (solved by SMT)
5.19/3.16	
5.19/3.16	      resulting limit problem: [solved]
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	      applying transformation rule (C) using substitution {B==-n}
5.19/3.16	
5.19/3.16	      resulting limit problem:
5.19/3.16	
5.19/3.16	      [solved]
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	   Solution:
5.19/3.16	
5.19/3.16	      B / -n
5.19/3.16	
5.19/3.16	   Resulting cost 21+5*n has complexity: Poly(n^1)
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Found new complexity Poly(n^1).
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	Obtained the following overall complexity (w.r.t. the length of the input n):
5.19/3.16	
5.19/3.16	   Complexity:  Poly(n^1)
5.19/3.16	
5.19/3.16	   Cpx degree:  1
5.19/3.16	
5.19/3.16	   Solved cost: 21+5*n
5.19/3.16	
5.19/3.16	   Rule cost:   21-5*B
5.19/3.16	
5.19/3.16	   Rule guard:  [ 2>=B ]
5.19/3.16	
5.19/3.16	
5.19/3.16	
5.19/3.16	WORST_CASE(Omega(n^1),?)
5.19/3.16	
5.19/3.16	
5.19/3.16	----------------------------------------
5.19/3.16	
5.19/3.16	(4)
5.19/3.16	BOUNDS(n^1, INF)
5.19/3.17	EOF