5.10/2.34	WORST_CASE(Omega(n^2), O(n^2))
5.10/2.35	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.10/2.35	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.10/2.35	
5.10/2.35	
5.10/2.35	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).
5.10/2.35	
5.10/2.35	(0) CpxIntTrs
5.10/2.35	(1) Koat Proof [FINISHED, 123 ms]
5.10/2.35	(2) BOUNDS(1, n^2)
5.10/2.35	(3) Loat Proof [FINISHED, 627 ms]
5.10/2.35	(4) BOUNDS(n^2, INF)
5.10/2.35	
5.10/2.35	
5.10/2.35	----------------------------------------
5.10/2.35	
5.10/2.35	(0)
5.10/2.35	Obligation:
5.10/2.35	Complexity Int TRS consisting of the following rules:
5.10/2.35	eval_while2_start(v_3, v_N, v_i_0, v_j_0) -> Com_1(eval_while2_bb0_in(v_3, v_N, v_i_0, v_j_0)) :|: TRUE
5.10/2.35	eval_while2_bb0_in(v_3, v_N, v_i_0, v_j_0) -> Com_1(eval_while2_0(v_3, v_N, v_i_0, v_j_0)) :|: TRUE
5.10/2.35	eval_while2_0(v_3, v_N, v_i_0, v_j_0) -> Com_1(eval_while2_1(v_3, v_N, v_i_0, v_j_0)) :|: TRUE
5.10/2.35	eval_while2_1(v_3, v_N, v_i_0, v_j_0) -> Com_1(eval_while2_2(v_3, v_N, v_i_0, v_j_0)) :|: TRUE
5.10/2.35	eval_while2_2(v_3, v_N, v_i_0, v_j_0) -> Com_1(eval_while2_3(v_3, v_N, v_i_0, v_j_0)) :|: TRUE
5.10/2.35	eval_while2_3(v_3, v_N, v_i_0, v_j_0) -> Com_1(eval_while2_4(v_3, v_N, v_i_0, v_j_0)) :|: TRUE
5.10/2.35	eval_while2_4(v_3, v_N, v_i_0, v_j_0) -> Com_1(eval_while2_bb1_in(v_3, v_N, v_N, v_j_0)) :|: TRUE
5.10/2.35	eval_while2_bb1_in(v_3, v_N, v_i_0, v_j_0) -> Com_1(eval_while2_bb2_in(v_3, v_N, v_i_0, v_N)) :|: v_i_0 > 0
5.10/2.35	eval_while2_bb1_in(v_3, v_N, v_i_0, v_j_0) -> Com_1(eval_while2_bb5_in(v_3, v_N, v_i_0, v_j_0)) :|: v_i_0 <= 0
5.10/2.35	eval_while2_bb2_in(v_3, v_N, v_i_0, v_j_0) -> Com_1(eval_while2_bb3_in(v_3, v_N, v_i_0, v_j_0)) :|: v_j_0 > 0
5.10/2.35	eval_while2_bb2_in(v_3, v_N, v_i_0, v_j_0) -> Com_1(eval_while2_bb4_in(v_3, v_N, v_i_0, v_j_0)) :|: v_j_0 <= 0
5.10/2.35	eval_while2_bb3_in(v_3, v_N, v_i_0, v_j_0) -> Com_1(eval_while2_bb2_in(v_3, v_N, v_i_0, v_j_0 - 1)) :|: TRUE
5.10/2.35	eval_while2_bb4_in(v_3, v_N, v_i_0, v_j_0) -> Com_1(eval_while2_8(v_i_0 - 1, v_N, v_i_0, v_j_0)) :|: TRUE
5.10/2.35	eval_while2_8(v_3, v_N, v_i_0, v_j_0) -> Com_1(eval_while2_9(v_3, v_N, v_i_0, v_j_0)) :|: TRUE
5.10/2.35	eval_while2_9(v_3, v_N, v_i_0, v_j_0) -> Com_1(eval_while2_bb1_in(v_3, v_N, v_3, v_j_0)) :|: TRUE
5.10/2.35	eval_while2_bb5_in(v_3, v_N, v_i_0, v_j_0) -> Com_1(eval_while2_stop(v_3, v_N, v_i_0, v_j_0)) :|: TRUE
5.10/2.35	
5.10/2.35	The start-symbols are:[eval_while2_start_4]
5.10/2.35	
5.10/2.35	
5.10/2.35	----------------------------------------
5.10/2.35	
5.10/2.35	(1) Koat Proof (FINISHED)
5.10/2.35	YES(?, 19*ar_1 + 2*ar_1^2 + 28)
5.10/2.35	
5.10/2.35	
5.10/2.35	
5.10/2.35	Initial complexity problem:
5.10/2.35	
5.10/2.35	1:	T:
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile20(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile21(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile22(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile23(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile24(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_1, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= 1 ]
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile28(ar_0, ar_1, ar_2, ar_0 - 1))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile29(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_3, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.10/2.35	
5.10/2.35		start location:	koat_start
5.10/2.35	
5.10/2.35		leaf cost:	0
5.10/2.35	
5.10/2.35	
5.10/2.35	
5.10/2.35	Repeatedly propagating knowledge in problem 1 produces the following problem:
5.10/2.35	
5.10/2.35	2:	T:
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)    evalwhile2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)    evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile20(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)    evalwhile20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile21(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)    evalwhile21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile22(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)    evalwhile22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile23(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)    evalwhile23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile24(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)    evalwhile24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_1, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= 1 ]
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile28(ar_0, ar_1, ar_2, ar_0 - 1))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile29(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_3, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.10/2.35	
5.10/2.35		start location:	koat_start
5.10/2.35	
5.10/2.35		leaf cost:	0
5.10/2.35	
5.10/2.35	
5.10/2.35	
5.10/2.35	A polynomial rank function with
5.10/2.35	
5.10/2.35		Pol(evalwhile2start) = 2
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb0in) = 2
5.10/2.35	
5.10/2.35		Pol(evalwhile20) = 2
5.10/2.35	
5.10/2.35		Pol(evalwhile21) = 2
5.10/2.35	
5.10/2.35		Pol(evalwhile22) = 2
5.10/2.35	
5.10/2.35		Pol(evalwhile23) = 2
5.10/2.35	
5.10/2.35		Pol(evalwhile24) = 2
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb1in) = 2
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb2in) = 2
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb5in) = 1
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb3in) = 2
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb4in) = 2
5.10/2.35	
5.10/2.35		Pol(evalwhile28) = 2
5.10/2.35	
5.10/2.35		Pol(evalwhile29) = 2
5.10/2.35	
5.10/2.35		Pol(evalwhile2stop) = 0
5.10/2.35	
5.10/2.35		Pol(koat_start) = 2
5.10/2.35	
5.10/2.35	orients all transitions weakly and the transitions
5.10/2.35	
5.10/2.35		evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35		evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.10/2.35	
5.10/2.35	strictly and produces the following problem:
5.10/2.35	
5.10/2.35	3:	T:
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)    evalwhile2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)    evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile20(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)    evalwhile20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile21(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)    evalwhile21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile22(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)    evalwhile22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile23(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)    evalwhile23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile24(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)    evalwhile24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_1, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= 1 ]
5.10/2.35	
5.10/2.35			(Comp: 2, Cost: 1)    evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile28(ar_0, ar_1, ar_2, ar_0 - 1))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile29(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)    evalwhile29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_3, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 2, Cost: 1)    evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.10/2.35	
5.10/2.35		start location:	koat_start
5.10/2.35	
5.10/2.35		leaf cost:	0
5.10/2.35	
5.10/2.35	
5.10/2.35	
5.10/2.35	A polynomial rank function with
5.10/2.35	
5.10/2.35		Pol(evalwhile2start) = V_2 + 1
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb0in) = V_2 + 1
5.10/2.35	
5.10/2.35		Pol(evalwhile20) = V_2 + 1
5.10/2.35	
5.10/2.35		Pol(evalwhile21) = V_2 + 1
5.10/2.35	
5.10/2.35		Pol(evalwhile22) = V_2 + 1
5.10/2.35	
5.10/2.35		Pol(evalwhile23) = V_2 + 1
5.10/2.35	
5.10/2.35		Pol(evalwhile24) = V_2 + 1
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb1in) = V_1 + 1
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb2in) = V_1
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb5in) = V_1
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb3in) = V_1
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb4in) = V_1
5.10/2.35	
5.10/2.35		Pol(evalwhile28) = V_4 + 1
5.10/2.35	
5.10/2.35		Pol(evalwhile29) = V_4 + 1
5.10/2.35	
5.10/2.35		Pol(evalwhile2stop) = V_1
5.10/2.35	
5.10/2.35		Pol(koat_start) = V_2 + 1
5.10/2.35	
5.10/2.35	orients all transitions weakly and the transition
5.10/2.35	
5.10/2.35		evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= 1 ]
5.10/2.35	
5.10/2.35	strictly and produces the following problem:
5.10/2.35	
5.10/2.35	4:	T:
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)           evalwhile2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)           evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile20(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)           evalwhile20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile21(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)           evalwhile21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile22(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)           evalwhile22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile23(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)           evalwhile23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile24(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)           evalwhile24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_1, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ar_1 + 1, Cost: 1)    evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= 1 ]
5.10/2.35	
5.10/2.35			(Comp: 2, Cost: 1)           evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)           evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)           evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)           evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)           evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile28(ar_0, ar_1, ar_2, ar_0 - 1))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)           evalwhile28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile29(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)           evalwhile29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_3, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 2, Cost: 1)           evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.10/2.35	
5.10/2.35		start location:	koat_start
5.10/2.35	
5.10/2.35		leaf cost:	0
5.10/2.35	
5.10/2.35	
5.10/2.35	
5.10/2.35	A polynomial rank function with
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb4in) = 3
5.10/2.35	
5.10/2.35		Pol(evalwhile28) = 2
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb3in) = 4
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb2in) = 4
5.10/2.35	
5.10/2.35		Pol(evalwhile29) = 1
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb1in) = 0
5.10/2.35	
5.10/2.35	and size complexities
5.10/2.35	
5.10/2.35		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
5.10/2.35	
5.10/2.35		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
5.10/2.35	
5.10/2.35		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
5.10/2.35	
5.10/2.35		S("evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
5.10/2.35	
5.10/2.35		S("evalwhile29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-0) = ?
5.10/2.35	
5.10/2.35		S("evalwhile29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-2) = ?
5.10/2.35	
5.10/2.35		S("evalwhile29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-3) = ?
5.10/2.35	
5.10/2.35		S("evalwhile28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile29(ar_0, ar_1, ar_2, ar_3))", 0-0) = ?
5.10/2.35	
5.10/2.35		S("evalwhile28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile29(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile29(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
5.10/2.35	
5.10/2.35		S("evalwhile28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile29(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile28(ar_0, ar_1, ar_2, ar_0 - 1))", 0-0) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile28(ar_0, ar_1, ar_2, ar_0 - 1))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile28(ar_0, ar_1, ar_2, ar_0 - 1))", 0-2) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile28(ar_0, ar_1, ar_2, ar_0 - 1))", 0-3) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1, ar_3))", 0-0) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1, ar_3))", 0-2) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1, ar_3))", 0-3) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-0) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-2) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-3) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-0) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-2) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-3) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= 1 ]", 0-0) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= 1 ]", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= 1 ]", 0-2) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= 1 ]", 0-3) = ?
5.10/2.35	
5.10/2.35		S("evalwhile24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_1, ar_1, ar_2, ar_3))", 0-0) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_1, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_1, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.10/2.35	
5.10/2.35		S("evalwhile24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_1, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.10/2.35	
5.10/2.35		S("evalwhile23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile24(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.10/2.35	
5.10/2.35		S("evalwhile23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile24(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile24(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.10/2.35	
5.10/2.35		S("evalwhile23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile24(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.10/2.35	
5.10/2.35		S("evalwhile22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile23(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.10/2.35	
5.10/2.35		S("evalwhile22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile23(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile23(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.10/2.35	
5.10/2.35		S("evalwhile22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile23(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.10/2.35	
5.10/2.35		S("evalwhile21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile22(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.10/2.35	
5.10/2.35		S("evalwhile21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile22(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile22(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.10/2.35	
5.10/2.35		S("evalwhile21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile22(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.10/2.35	
5.10/2.35		S("evalwhile20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile21(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.10/2.35	
5.10/2.35		S("evalwhile20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile21(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile21(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.10/2.35	
5.10/2.35		S("evalwhile20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile21(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.10/2.35	
5.10/2.35		S("evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile20(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.10/2.35	
5.10/2.35		S("evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile20(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile20(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.10/2.35	
5.10/2.35		S("evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile20(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.10/2.35	
5.10/2.35		S("evalwhile2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.10/2.35	
5.10/2.35		S("evalwhile2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.10/2.35	
5.10/2.35		S("evalwhile2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.10/2.35	
5.10/2.35	orients the transitions
5.10/2.35	
5.10/2.35		evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile28(ar_0, ar_1, ar_2, ar_0 - 1))
5.10/2.35	
5.10/2.35		evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1, ar_3))
5.10/2.35	
5.10/2.35		evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
5.10/2.35	
5.10/2.35		evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.10/2.35	
5.10/2.35		evalwhile29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_3, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35		evalwhile28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile29(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35	weakly and the transitions
5.10/2.35	
5.10/2.35		evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile28(ar_0, ar_1, ar_2, ar_0 - 1))
5.10/2.35	
5.10/2.35		evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
5.10/2.35	
5.10/2.35		evalwhile29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_3, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35		evalwhile28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile29(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35	strictly and produces the following problem:
5.10/2.35	
5.10/2.35	5:	T:
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)             evalwhile2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)             evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile20(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)             evalwhile20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile21(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)             evalwhile21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile22(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)             evalwhile22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile23(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)             evalwhile23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile24(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)             evalwhile24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_1, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ar_1 + 1, Cost: 1)      evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= 1 ]
5.10/2.35	
5.10/2.35			(Comp: 2, Cost: 1)             evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)             evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.10/2.35	
5.10/2.35			(Comp: 4*ar_1 + 4, Cost: 1)    evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)             evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 4*ar_1 + 4, Cost: 1)    evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile28(ar_0, ar_1, ar_2, ar_0 - 1))
5.10/2.35	
5.10/2.35			(Comp: 4*ar_1 + 4, Cost: 1)    evalwhile28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile29(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 4*ar_1 + 4, Cost: 1)    evalwhile29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_3, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 2, Cost: 1)             evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.10/2.35	
5.10/2.35		start location:	koat_start
5.10/2.35	
5.10/2.35		leaf cost:	0
5.10/2.35	
5.10/2.35	
5.10/2.35	
5.10/2.35	A polynomial rank function with
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb3in) = V_3 - 1
5.10/2.35	
5.10/2.35		Pol(evalwhile2bb2in) = V_3
5.10/2.35	
5.10/2.35	and size complexities
5.10/2.35	
5.10/2.35		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
5.10/2.35	
5.10/2.35		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
5.10/2.35	
5.10/2.35		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
5.10/2.35	
5.10/2.35		S("evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = 5*ar_1 + 2500
5.10/2.35	
5.10/2.35		S("evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = 5*ar_1 + 5*ar_3 + 12500
5.10/2.35	
5.10/2.35		S("evalwhile29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-0) = 5*ar_1 + 100
5.10/2.35	
5.10/2.35		S("evalwhile29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-2) = ?
5.10/2.35	
5.10/2.35		S("evalwhile29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-3) = 5*ar_1 + 500
5.10/2.35	
5.10/2.35		S("evalwhile28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile29(ar_0, ar_1, ar_2, ar_3))", 0-0) = 5*ar_1 + 2500
5.10/2.35	
5.10/2.35		S("evalwhile28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile29(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile29(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
5.10/2.35	
5.10/2.35		S("evalwhile28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile29(ar_0, ar_1, ar_2, ar_3))", 0-3) = 5*ar_1 + 100
5.10/2.35	
5.10/2.35		S("evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile28(ar_0, ar_1, ar_2, ar_0 - 1))", 0-0) = 5*ar_1 + 500
5.10/2.35	
5.10/2.35		S("evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile28(ar_0, ar_1, ar_2, ar_0 - 1))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile28(ar_0, ar_1, ar_2, ar_0 - 1))", 0-2) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile28(ar_0, ar_1, ar_2, ar_0 - 1))", 0-3) = 5*ar_1 + 100
5.10/2.35	
5.10/2.35		S("evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1, ar_3))", 0-0) = 5*ar_1 + 100
5.10/2.35	
5.10/2.35		S("evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1, ar_3))", 0-2) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1, ar_3))", 0-3) = 5*ar_1 + 5*ar_3 + 12500
5.10/2.35	
5.10/2.35		S("evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-0) = 5*ar_1 + 100
5.10/2.35	
5.10/2.35		S("evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-2) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-3) = 5*ar_1 + 5*ar_3 + 62500
5.10/2.35	
5.10/2.35		S("evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-0) = 5*ar_1 + 100
5.10/2.35	
5.10/2.35		S("evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-2) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-3) = 5*ar_1 + 5*ar_3 + 12500
5.10/2.35	
5.10/2.35		S("evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = 5*ar_1 + 500
5.10/2.35	
5.10/2.35		S("evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ?
5.10/2.35	
5.10/2.35		S("evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = 5*ar_1 + 5*ar_3 + 2500
5.10/2.35	
5.10/2.35		S("evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= 1 ]", 0-0) = 5*ar_1 + 100
5.10/2.35	
5.10/2.35		S("evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= 1 ]", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= 1 ]", 0-2) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= 1 ]", 0-3) = 5*ar_1 + 5*ar_3 + 2500
5.10/2.35	
5.10/2.35		S("evalwhile24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_1, ar_1, ar_2, ar_3))", 0-0) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_1, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_1, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.10/2.35	
5.10/2.35		S("evalwhile24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_1, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.10/2.35	
5.10/2.35		S("evalwhile23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile24(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.10/2.35	
5.10/2.35		S("evalwhile23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile24(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile24(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.10/2.35	
5.10/2.35		S("evalwhile23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile24(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.10/2.35	
5.10/2.35		S("evalwhile22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile23(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.10/2.35	
5.10/2.35		S("evalwhile22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile23(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile23(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.10/2.35	
5.10/2.35		S("evalwhile22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile23(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.10/2.35	
5.10/2.35		S("evalwhile21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile22(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.10/2.35	
5.10/2.35		S("evalwhile21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile22(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile22(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.10/2.35	
5.10/2.35		S("evalwhile21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile22(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.10/2.35	
5.10/2.35		S("evalwhile20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile21(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.10/2.35	
5.10/2.35		S("evalwhile20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile21(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile21(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.10/2.35	
5.10/2.35		S("evalwhile20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile21(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.10/2.35	
5.10/2.35		S("evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile20(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.10/2.35	
5.10/2.35		S("evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile20(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile20(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.10/2.35	
5.10/2.35		S("evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile20(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.10/2.35	
5.10/2.35		S("evalwhile2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.10/2.35	
5.10/2.35		S("evalwhile2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.10/2.35	
5.10/2.35		S("evalwhile2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.10/2.35	
5.10/2.35		S("evalwhile2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.10/2.35	
5.10/2.35	orients the transitions
5.10/2.35	
5.10/2.35		evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1, ar_3))
5.10/2.35	
5.10/2.35		evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.10/2.35	
5.10/2.35	weakly and the transition
5.10/2.35	
5.10/2.35		evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.10/2.35	
5.10/2.35	strictly and produces the following problem:
5.10/2.35	
5.10/2.35	6:	T:
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)                evalwhile2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)                evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile20(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)                evalwhile20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile21(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)                evalwhile21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile22(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)                evalwhile22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile23(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)                evalwhile23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile24(ar_0, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 1, Cost: 1)                evalwhile24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_1, ar_1, ar_2, ar_3))
5.10/2.35	
5.10/2.35			(Comp: ar_1 + 1, Cost: 1)         evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= 1 ]
5.10/2.35	
5.10/2.35			(Comp: 2, Cost: 1)                evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.10/2.35	
5.10/2.35			(Comp: ar_1^2 + ar_1, Cost: 1)    evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.10/2.35	
5.10/2.35			(Comp: 4*ar_1 + 4, Cost: 1)       evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
5.10/2.35	
5.10/2.35			(Comp: ?, Cost: 1)                evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1, ar_3))
5.10/2.35	
5.10/2.35			(Comp: 4*ar_1 + 4, Cost: 1)       evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile28(ar_0, ar_1, ar_2, ar_0 - 1))
5.10/2.35	
5.10/2.35			(Comp: 4*ar_1 + 4, Cost: 1)       evalwhile28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile29(ar_0, ar_1, ar_2, ar_3))
5.10/2.36	
5.10/2.36			(Comp: 4*ar_1 + 4, Cost: 1)       evalwhile29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_3, ar_1, ar_2, ar_3))
5.10/2.36	
5.10/2.36			(Comp: 2, Cost: 1)                evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2, ar_3))
5.10/2.36	
5.10/2.36			(Comp: 1, Cost: 0)                koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.10/2.36	
5.10/2.36		start location:	koat_start
5.10/2.36	
5.10/2.36		leaf cost:	0
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Repeatedly propagating knowledge in problem 6 produces the following problem:
5.10/2.36	
5.10/2.36	7:	T:
5.10/2.36	
5.10/2.36			(Comp: 1, Cost: 1)                evalwhile2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3))
5.10/2.36	
5.10/2.36			(Comp: 1, Cost: 1)                evalwhile2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile20(ar_0, ar_1, ar_2, ar_3))
5.10/2.36	
5.10/2.36			(Comp: 1, Cost: 1)                evalwhile20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile21(ar_0, ar_1, ar_2, ar_3))
5.10/2.36	
5.10/2.36			(Comp: 1, Cost: 1)                evalwhile21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile22(ar_0, ar_1, ar_2, ar_3))
5.10/2.36	
5.10/2.36			(Comp: 1, Cost: 1)                evalwhile22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile23(ar_0, ar_1, ar_2, ar_3))
5.10/2.36	
5.10/2.36			(Comp: 1, Cost: 1)                evalwhile23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile24(ar_0, ar_1, ar_2, ar_3))
5.10/2.36	
5.10/2.36			(Comp: 1, Cost: 1)                evalwhile24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_1, ar_1, ar_2, ar_3))
5.10/2.36	
5.10/2.36			(Comp: ar_1 + 1, Cost: 1)         evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= 1 ]
5.10/2.36	
5.10/2.36			(Comp: 2, Cost: 1)                evalwhile2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.10/2.36	
5.10/2.36			(Comp: ar_1^2 + ar_1, Cost: 1)    evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.10/2.36	
5.10/2.36			(Comp: 4*ar_1 + 4, Cost: 1)       evalwhile2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
5.10/2.36	
5.10/2.36			(Comp: ar_1^2 + ar_1, Cost: 1)    evalwhile2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1, ar_3))
5.10/2.36	
5.10/2.36			(Comp: 4*ar_1 + 4, Cost: 1)       evalwhile2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile28(ar_0, ar_1, ar_2, ar_0 - 1))
5.10/2.36	
5.10/2.36			(Comp: 4*ar_1 + 4, Cost: 1)       evalwhile28(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile29(ar_0, ar_1, ar_2, ar_3))
5.10/2.36	
5.10/2.36			(Comp: 4*ar_1 + 4, Cost: 1)       evalwhile29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2bb1in(ar_3, ar_1, ar_2, ar_3))
5.10/2.36	
5.10/2.36			(Comp: 2, Cost: 1)                evalwhile2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2, ar_3))
5.10/2.36	
5.10/2.36			(Comp: 1, Cost: 0)                koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwhile2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.10/2.36	
5.10/2.36		start location:	koat_start
5.10/2.36	
5.10/2.36		leaf cost:	0
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Complexity upper bound 19*ar_1 + 2*ar_1^2 + 28
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Time: 0.168 sec (SMT: 0.126 sec)
5.10/2.36	
5.10/2.36	
5.10/2.36	----------------------------------------
5.10/2.36	
5.10/2.36	(2)
5.10/2.36	BOUNDS(1, n^2)
5.10/2.36	
5.10/2.36	----------------------------------------
5.10/2.36	
5.10/2.36	(3) Loat Proof (FINISHED)
5.10/2.36	
5.10/2.36	
5.10/2.36	### Pre-processing the ITS problem ###
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Initial linear ITS problem
5.10/2.36	
5.10/2.36	   Start location: evalwhile2start
5.10/2.36	
5.10/2.36	      0: evalwhile2start -> evalwhile2bb0in : [], cost: 1
5.10/2.36	
5.10/2.36	      1: evalwhile2bb0in -> evalwhile20 : [], cost: 1
5.10/2.36	
5.10/2.36	      2: evalwhile20 -> evalwhile21 : [], cost: 1
5.10/2.36	
5.10/2.36	      3: evalwhile21 -> evalwhile22 : [], cost: 1
5.10/2.36	
5.10/2.36	      4: evalwhile22 -> evalwhile23 : [], cost: 1
5.10/2.36	
5.10/2.36	      5: evalwhile23 -> evalwhile24 : [], cost: 1
5.10/2.36	
5.10/2.36	      6: evalwhile24 -> evalwhile2bb1in : A'=B, [], cost: 1
5.10/2.36	
5.10/2.36	      7: evalwhile2bb1in -> evalwhile2bb2in : C'=B, [ A>=1 ], cost: 1
5.10/2.36	
5.10/2.36	      8: evalwhile2bb1in -> evalwhile2bb5in : [ 0>=A ], cost: 1
5.10/2.36	
5.10/2.36	      9: evalwhile2bb2in -> evalwhile2bb3in : [ C>=1 ], cost: 1
5.10/2.36	
5.10/2.36	     10: evalwhile2bb2in -> evalwhile2bb4in : [ 0>=C ], cost: 1
5.10/2.36	
5.10/2.36	     11: evalwhile2bb3in -> evalwhile2bb2in : C'=-1+C, [], cost: 1
5.10/2.36	
5.10/2.36	     12: evalwhile2bb4in -> evalwhile28 : D'=-1+A, [], cost: 1
5.10/2.36	
5.10/2.36	     13: evalwhile28 -> evalwhile29 : [], cost: 1
5.10/2.36	
5.10/2.36	     14: evalwhile29 -> evalwhile2bb1in : A'=D, [], cost: 1
5.10/2.36	
5.10/2.36	     15: evalwhile2bb5in -> evalwhile2stop : [], cost: 1
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Removed unreachable and leaf rules:
5.10/2.36	
5.10/2.36	   Start location: evalwhile2start
5.10/2.36	
5.10/2.36	      0: evalwhile2start -> evalwhile2bb0in : [], cost: 1
5.10/2.36	
5.10/2.36	      1: evalwhile2bb0in -> evalwhile20 : [], cost: 1
5.10/2.36	
5.10/2.36	      2: evalwhile20 -> evalwhile21 : [], cost: 1
5.10/2.36	
5.10/2.36	      3: evalwhile21 -> evalwhile22 : [], cost: 1
5.10/2.36	
5.10/2.36	      4: evalwhile22 -> evalwhile23 : [], cost: 1
5.10/2.36	
5.10/2.36	      5: evalwhile23 -> evalwhile24 : [], cost: 1
5.10/2.36	
5.10/2.36	      6: evalwhile24 -> evalwhile2bb1in : A'=B, [], cost: 1
5.10/2.36	
5.10/2.36	      7: evalwhile2bb1in -> evalwhile2bb2in : C'=B, [ A>=1 ], cost: 1
5.10/2.36	
5.10/2.36	      9: evalwhile2bb2in -> evalwhile2bb3in : [ C>=1 ], cost: 1
5.10/2.36	
5.10/2.36	     10: evalwhile2bb2in -> evalwhile2bb4in : [ 0>=C ], cost: 1
5.10/2.36	
5.10/2.36	     11: evalwhile2bb3in -> evalwhile2bb2in : C'=-1+C, [], cost: 1
5.10/2.36	
5.10/2.36	     12: evalwhile2bb4in -> evalwhile28 : D'=-1+A, [], cost: 1
5.10/2.36	
5.10/2.36	     13: evalwhile28 -> evalwhile29 : [], cost: 1
5.10/2.36	
5.10/2.36	     14: evalwhile29 -> evalwhile2bb1in : A'=D, [], cost: 1
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	### Simplification by acceleration and chaining ###
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Eliminated locations (on linear paths):
5.10/2.36	
5.10/2.36	   Start location: evalwhile2start
5.10/2.36	
5.10/2.36	     21: evalwhile2start -> evalwhile2bb1in : A'=B, [], cost: 7
5.10/2.36	
5.10/2.36	      7: evalwhile2bb1in -> evalwhile2bb2in : C'=B, [ A>=1 ], cost: 1
5.10/2.36	
5.10/2.36	     22: evalwhile2bb2in -> evalwhile2bb2in : C'=-1+C, [ C>=1 ], cost: 2
5.10/2.36	
5.10/2.36	     25: evalwhile2bb2in -> evalwhile2bb1in : A'=-1+A, D'=-1+A, [ 0>=C ], cost: 4
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Accelerating simple loops of location 8.
5.10/2.36	
5.10/2.36	   Accelerating the following rules:
5.10/2.36	
5.10/2.36	     22: evalwhile2bb2in -> evalwhile2bb2in : C'=-1+C, [ C>=1 ], cost: 2
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	   Accelerated rule 22 with metering function C, yielding the new rule 26.
5.10/2.36	
5.10/2.36	   Removing the simple loops: 22.
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Accelerated all simple loops using metering functions (where possible):
5.10/2.36	
5.10/2.36	   Start location: evalwhile2start
5.10/2.36	
5.10/2.36	     21: evalwhile2start -> evalwhile2bb1in : A'=B, [], cost: 7
5.10/2.36	
5.10/2.36	      7: evalwhile2bb1in -> evalwhile2bb2in : C'=B, [ A>=1 ], cost: 1
5.10/2.36	
5.10/2.36	     25: evalwhile2bb2in -> evalwhile2bb1in : A'=-1+A, D'=-1+A, [ 0>=C ], cost: 4
5.10/2.36	
5.10/2.36	     26: evalwhile2bb2in -> evalwhile2bb2in : C'=0, [ C>=1 ], cost: 2*C
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Chained accelerated rules (with incoming rules):
5.10/2.36	
5.10/2.36	   Start location: evalwhile2start
5.10/2.36	
5.10/2.36	     21: evalwhile2start -> evalwhile2bb1in : A'=B, [], cost: 7
5.10/2.36	
5.10/2.36	      7: evalwhile2bb1in -> evalwhile2bb2in : C'=B, [ A>=1 ], cost: 1
5.10/2.36	
5.10/2.36	     27: evalwhile2bb1in -> evalwhile2bb2in : C'=0, [ A>=1 && B>=1 ], cost: 1+2*B
5.10/2.36	
5.10/2.36	     25: evalwhile2bb2in -> evalwhile2bb1in : A'=-1+A, D'=-1+A, [ 0>=C ], cost: 4
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Eliminated locations (on tree-shaped paths):
5.10/2.36	
5.10/2.36	   Start location: evalwhile2start
5.10/2.36	
5.10/2.36	     21: evalwhile2start -> evalwhile2bb1in : A'=B, [], cost: 7
5.10/2.36	
5.10/2.36	     28: evalwhile2bb1in -> evalwhile2bb1in : A'=-1+A, C'=B, D'=-1+A, [ A>=1 && 0>=B ], cost: 5
5.10/2.36	
5.10/2.36	     29: evalwhile2bb1in -> evalwhile2bb1in : A'=-1+A, C'=0, D'=-1+A, [ A>=1 && B>=1 ], cost: 5+2*B
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Accelerating simple loops of location 7.
5.10/2.36	
5.10/2.36	   Accelerating the following rules:
5.10/2.36	
5.10/2.36	     28: evalwhile2bb1in -> evalwhile2bb1in : A'=-1+A, C'=B, D'=-1+A, [ A>=1 && 0>=B ], cost: 5
5.10/2.36	
5.10/2.36	     29: evalwhile2bb1in -> evalwhile2bb1in : A'=-1+A, C'=0, D'=-1+A, [ A>=1 && B>=1 ], cost: 5+2*B
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	   Accelerated rule 28 with metering function A, yielding the new rule 30.
5.10/2.36	
5.10/2.36	   Accelerated rule 29 with metering function A, yielding the new rule 31.
5.10/2.36	
5.10/2.36	   Removing the simple loops: 28 29.
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Accelerated all simple loops using metering functions (where possible):
5.10/2.36	
5.10/2.36	   Start location: evalwhile2start
5.10/2.36	
5.10/2.36	     21: evalwhile2start -> evalwhile2bb1in : A'=B, [], cost: 7
5.10/2.36	
5.10/2.36	     30: evalwhile2bb1in -> evalwhile2bb1in : A'=0, C'=B, D'=0, [ A>=1 && 0>=B ], cost: 5*A
5.10/2.36	
5.10/2.36	     31: evalwhile2bb1in -> evalwhile2bb1in : A'=0, C'=0, D'=0, [ A>=1 && B>=1 ], cost: 5*A+2*A*B
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Chained accelerated rules (with incoming rules):
5.10/2.36	
5.10/2.36	   Start location: evalwhile2start
5.10/2.36	
5.10/2.36	     21: evalwhile2start -> evalwhile2bb1in : A'=B, [], cost: 7
5.10/2.36	
5.10/2.36	     32: evalwhile2start -> evalwhile2bb1in : A'=0, C'=0, D'=0, [ B>=1 ], cost: 7+2*B^2+5*B
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Removed unreachable locations (and leaf rules with constant cost):
5.10/2.36	
5.10/2.36	   Start location: evalwhile2start
5.10/2.36	
5.10/2.36	     32: evalwhile2start -> evalwhile2bb1in : A'=0, C'=0, D'=0, [ B>=1 ], cost: 7+2*B^2+5*B
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	### Computing asymptotic complexity ###
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Fully simplified ITS problem
5.10/2.36	
5.10/2.36	   Start location: evalwhile2start
5.10/2.36	
5.10/2.36	     32: evalwhile2start -> evalwhile2bb1in : A'=0, C'=0, D'=0, [ B>=1 ], cost: 7+2*B^2+5*B
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Computing asymptotic complexity for rule 32
5.10/2.36	
5.10/2.36	   Solved the limit problem by the following transformations:
5.10/2.36	
5.10/2.36	      Created initial limit problem:
5.10/2.36	
5.10/2.36	      7+2*B^2+5*B (+), B (+/+!) [not solved]
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	      removing all constraints (solved by SMT)
5.10/2.36	
5.10/2.36	      resulting limit problem: [solved]
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	      applying transformation rule (C) using substitution {B==n}
5.10/2.36	
5.10/2.36	      resulting limit problem:
5.10/2.36	
5.10/2.36	      [solved]
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	   Solution:
5.10/2.36	
5.10/2.36	      B / n
5.10/2.36	
5.10/2.36	   Resulting cost 7+2*n^2+5*n has complexity: Poly(n^2)
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Found new complexity Poly(n^2).
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	Obtained the following overall complexity (w.r.t. the length of the input n):
5.10/2.36	
5.10/2.36	   Complexity:  Poly(n^2)
5.10/2.36	
5.10/2.36	   Cpx degree:  2
5.10/2.36	
5.10/2.36	   Solved cost: 7+2*n^2+5*n
5.10/2.36	
5.10/2.36	   Rule cost:   7+2*B^2+5*B
5.10/2.36	
5.10/2.36	   Rule guard:  [ B>=1 ]
5.10/2.36	
5.10/2.36	
5.10/2.36	
5.10/2.36	WORST_CASE(Omega(n^2),?)
5.10/2.36	
5.10/2.36	
5.10/2.36	----------------------------------------
5.10/2.36	
5.10/2.36	(4)
5.10/2.36	BOUNDS(n^2, INF)
5.10/2.37	EOF