5.27/2.43	WORST_CASE(Omega(n^2), O(n^2))
5.34/2.44	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.34/2.44	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.34/2.44	
5.34/2.44	
5.34/2.44	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).
5.34/2.44	
5.34/2.44	(0) CpxIntTrs
5.34/2.44	(1) Koat Proof [FINISHED, 225 ms]
5.34/2.44	(2) BOUNDS(1, n^2)
5.34/2.44	(3) Loat Proof [FINISHED, 800 ms]
5.34/2.44	(4) BOUNDS(n^2, INF)
5.34/2.44	
5.34/2.44	
5.34/2.44	----------------------------------------
5.34/2.44	
5.34/2.44	(0)
5.34/2.44	Obligation:
5.34/2.44	Complexity Int TRS consisting of the following rules:
5.34/2.44	eval_ax_start(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb0_in(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE
5.34/2.44	eval_ax_bb0_in(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_0(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE
5.34/2.44	eval_ax_0(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_1(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE
5.34/2.44	eval_ax_1(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_2(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE
5.34/2.44	eval_ax_2(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_3(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE
5.34/2.44	eval_ax_3(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_4(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE
5.34/2.44	eval_ax_4(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_5(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE
5.34/2.44	eval_ax_5(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_6(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE
5.34/2.44	eval_ax_6(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb1_in(0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE
5.34/2.44	eval_ax_bb1_in(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb2_in(v__0, 0, v_3, v_i, v_j, v_n)) :|: TRUE
5.34/2.44	eval_ax_bb2_in(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb3_in(v__0, v__01, v_3, v_i, v_j, v_n)) :|: v__01 < v_n - 1
5.34/2.44	eval_ax_bb2_in(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb4_in(v__0, v__01, v_3, v_i, v_j, v_n)) :|: v__01 >= v_n - 1
5.34/2.44	eval_ax_bb3_in(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb2_in(v__0, v__01 + 1, v_3, v_i, v_j, v_n)) :|: TRUE
5.34/2.44	eval_ax_bb4_in(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_12(v__0, v__01, v__0 + 1, v_i, v_j, v_n)) :|: TRUE
5.34/2.44	eval_ax_12(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_13(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE
5.34/2.44	eval_ax_13(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb1_in(v_3, v__01, v_3, v_i, v_j, v_n)) :|: v__01 >= v_n - 1 && v_3 < v_n - 1
5.34/2.44	eval_ax_13(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb5_in(v__0, v__01, v_3, v_i, v_j, v_n)) :|: v__01 < v_n - 1
5.34/2.44	eval_ax_13(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb5_in(v__0, v__01, v_3, v_i, v_j, v_n)) :|: v_3 >= v_n - 1
5.34/2.44	eval_ax_bb5_in(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_stop(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE
5.34/2.44	
5.34/2.44	The start-symbols are:[eval_ax_start_6]
5.34/2.44	
5.34/2.44	
5.34/2.44	----------------------------------------
5.34/2.44	
5.34/2.44	(1) Koat Proof (FINISHED)
5.34/2.44	YES(?, 15*ar_2 + 2*ar_2^2 + 27)
5.34/2.44	
5.34/2.44	
5.34/2.44	
5.34/2.44	Initial complexity problem:
5.34/2.44	
5.34/2.44	1:	T:
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax0(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalax0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax1(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalax1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax2(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalax2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax3(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalax3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax4(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalax4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax5(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalax5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax6(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalax6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, 0, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\ ar_2 >= ar_3 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.34/2.44	
5.34/2.44		start location:	koat_start
5.34/2.44	
5.34/2.44		leaf cost:	0
5.34/2.44	
5.34/2.44	
5.34/2.44	
5.34/2.44	Repeatedly propagating knowledge in problem 1 produces the following problem:
5.34/2.44	
5.34/2.44	2:	T:
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalaxstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalaxbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax0(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalax0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax1(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalax1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax2(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalax2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax3(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalax3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax4(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalax4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax5(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalax5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax6(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalax6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, 0, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\ ar_2 >= ar_3 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.34/2.44	
5.34/2.44		start location:	koat_start
5.34/2.44	
5.34/2.44		leaf cost:	0
5.34/2.44	
5.34/2.44	
5.34/2.44	
5.34/2.44	A polynomial rank function with
5.34/2.44	
5.34/2.44		Pol(evalaxstart) = 2
5.34/2.44	
5.34/2.44		Pol(evalaxbb0in) = 2
5.34/2.44	
5.34/2.44		Pol(evalax0) = 2
5.34/2.44	
5.34/2.44		Pol(evalax1) = 2
5.34/2.44	
5.34/2.44		Pol(evalax2) = 2
5.34/2.44	
5.34/2.44		Pol(evalax3) = 2
5.34/2.44	
5.34/2.44		Pol(evalax4) = 2
5.34/2.44	
5.34/2.44		Pol(evalax5) = 2
5.34/2.44	
5.34/2.44		Pol(evalax6) = 2
5.34/2.44	
5.34/2.44		Pol(evalaxbb1in) = 2
5.34/2.44	
5.34/2.44		Pol(evalaxbb2in) = 2
5.34/2.44	
5.34/2.44		Pol(evalaxbb3in) = 2
5.34/2.44	
5.34/2.44		Pol(evalaxbb4in) = 2
5.34/2.44	
5.34/2.44		Pol(evalax12) = 2
5.34/2.44	
5.34/2.44		Pol(evalax13) = 2
5.34/2.44	
5.34/2.44		Pol(evalaxbb5in) = 1
5.34/2.44	
5.34/2.44		Pol(evalaxstop) = 0
5.34/2.44	
5.34/2.44		Pol(koat_start) = 2
5.34/2.44	
5.34/2.44	orients all transitions weakly and the transitions
5.34/2.44	
5.34/2.44		evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44		evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44		evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44	strictly and produces the following problem:
5.34/2.44	
5.34/2.44	3:	T:
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalaxstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalaxbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax0(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalax0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax1(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalax1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax2(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalax2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax3(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalax3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax4(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalax4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax5(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalax5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax6(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)    evalax6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, 0, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)    evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\ ar_2 >= ar_3 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)    evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)    evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)    evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.34/2.44	
5.34/2.44		start location:	koat_start
5.34/2.44	
5.34/2.44		leaf cost:	0
5.34/2.44	
5.34/2.44	
5.34/2.44	
5.34/2.44	A polynomial rank function with
5.34/2.44	
5.34/2.44		Pol(evalaxstart) = V_3
5.34/2.44	
5.34/2.44		Pol(evalaxbb0in) = V_3
5.34/2.44	
5.34/2.44		Pol(evalax0) = V_3
5.34/2.44	
5.34/2.44		Pol(evalax1) = V_3
5.34/2.44	
5.34/2.44		Pol(evalax2) = V_3
5.34/2.44	
5.34/2.44		Pol(evalax3) = V_3
5.34/2.44	
5.34/2.44		Pol(evalax4) = V_3
5.34/2.44	
5.34/2.44		Pol(evalax5) = V_3
5.34/2.44	
5.34/2.44		Pol(evalax6) = V_3
5.34/2.44	
5.34/2.44		Pol(evalaxbb1in) = -V_1 + V_3 - 1
5.34/2.44	
5.34/2.44		Pol(evalaxbb2in) = -V_1 + V_3 - 1
5.34/2.44	
5.34/2.44		Pol(evalaxbb3in) = -V_1 + V_3 - 1
5.34/2.44	
5.34/2.44		Pol(evalaxbb4in) = -V_1 + V_3 - 1
5.34/2.44	
5.34/2.44		Pol(evalax12) = V_3 - V_4
5.34/2.44	
5.34/2.44		Pol(evalax13) = V_3 - V_4
5.34/2.44	
5.34/2.44		Pol(evalaxbb5in) = V_3 - V_4
5.34/2.44	
5.34/2.44		Pol(evalaxstop) = V_3 - V_4
5.34/2.44	
5.34/2.44		Pol(koat_start) = V_3
5.34/2.44	
5.34/2.44	orients all transitions weakly and the transition
5.34/2.44	
5.34/2.44		evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\ ar_2 >= ar_3 + 2 ]
5.34/2.44	
5.34/2.44	strictly and produces the following problem:
5.34/2.44	
5.34/2.44	4:	T:
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)       evalaxstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)       evalaxbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax0(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)       evalax0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax1(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)       evalax1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax2(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)       evalax2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax3(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)       evalax3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax4(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)       evalax4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax5(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)       evalax5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax6(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)       evalax6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)       evalaxbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, 0, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)       evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)       evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)       evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)       evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)       evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ar_2, Cost: 1)    evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\ ar_2 >= ar_3 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)       evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)       evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)       evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.34/2.44	
5.34/2.44		start location:	koat_start
5.34/2.44	
5.34/2.44		leaf cost:	0
5.34/2.44	
5.34/2.44	
5.34/2.44	
5.34/2.44	Repeatedly propagating knowledge in problem 4 produces the following problem:
5.34/2.44	
5.34/2.44	5:	T:
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)           evalaxstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)           evalaxbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax0(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)           evalax0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax1(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)           evalax1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax2(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)           evalax2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax3(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)           evalax3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax4(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)           evalax4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax5(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)           evalax5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax6(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)           evalax6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ar_2 + 1, Cost: 1)    evalaxbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, 0, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)           evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)           evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)           evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)           evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)           evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ar_2, Cost: 1)        evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\ ar_2 >= ar_3 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)           evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)           evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)           evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.34/2.44	
5.34/2.44		start location:	koat_start
5.34/2.44	
5.34/2.44		leaf cost:	0
5.34/2.44	
5.34/2.44	
5.34/2.44	
5.34/2.44	A polynomial rank function with
5.34/2.44	
5.34/2.44		Pol(evalaxbb4in) = 2
5.34/2.44	
5.34/2.44		Pol(evalax12) = 1
5.34/2.44	
5.34/2.44		Pol(evalaxbb3in) = 3
5.34/2.44	
5.34/2.44		Pol(evalaxbb2in) = 3
5.34/2.44	
5.34/2.44		Pol(evalax13) = 0
5.34/2.44	
5.34/2.44	and size complexities
5.34/2.44	
5.34/2.44		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ]", 0-0) = ?
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ]", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ]", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ]", 0-3) = ?
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]", 0-0) = ?
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]", 0-3) = ?
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\\ ar_2 >= ar_3 + 2 ]", 0-0) = ?
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\\ ar_2 >= ar_3 + 2 ]", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\\ ar_2 >= ar_3 + 2 ]", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\\ ar_2 >= ar_3 + 2 ]", 0-3) = ?
5.34/2.44	
5.34/2.44		S("evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))", 0-0) = ?
5.34/2.44	
5.34/2.44		S("evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))", 0-0) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))", 0-3) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))", 0-0) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))", 0-3) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]", 0-0) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]", 0-3) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]", 0-0) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]", 0-3) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, 0, ar_2, ar_3))", 0-0) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, 0, ar_2, ar_3))", 0-1) = 0
5.34/2.44	
5.34/2.44		S("evalaxbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, 0, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalaxbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, 0, ar_2, ar_3))", 0-3) = ?
5.34/2.44	
5.34/2.44		S("evalax6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(0, ar_1, ar_2, ar_3))", 0-0) = 0
5.34/2.44	
5.34/2.44		S("evalax6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalax6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalax5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax6(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("evalax5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax6(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalax5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax6(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax6(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalax4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax5(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("evalax4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax5(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalax4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax5(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax5(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalax3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax4(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("evalax3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax4(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalax3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax4(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax4(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalax2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax3(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("evalax2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax3(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalax2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax3(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax3(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalax1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax2(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("evalax1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax2(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalax1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax2(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax2(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalax0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax1(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("evalax0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax1(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalax0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax1(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax1(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalaxbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax0(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("evalaxbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax0(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalaxbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax0(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalaxbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax0(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalaxstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("evalaxstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalaxstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalaxstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44	orients the transitions
5.34/2.44	
5.34/2.44		evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))
5.34/2.44	
5.34/2.44		evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))
5.34/2.44	
5.34/2.44		evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44		evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44		evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44	weakly and the transitions
5.34/2.44	
5.34/2.44		evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))
5.34/2.44	
5.34/2.44		evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44		evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44	strictly and produces the following problem:
5.34/2.44	
5.34/2.44	6:	T:
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)             evalaxstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)             evalaxbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax0(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)             evalax0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax1(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)             evalax1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax2(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)             evalax2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax3(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)             evalax3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax4(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)             evalax4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax5(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)             evalax5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax6(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)             evalax6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ar_2 + 1, Cost: 1)      evalaxbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, 0, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)             evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: 3*ar_2 + 3, Cost: 1)    evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)             evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 3*ar_2 + 3, Cost: 1)    evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))
5.34/2.44	
5.34/2.44			(Comp: 3*ar_2 + 3, Cost: 1)    evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ar_2, Cost: 1)          evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\ ar_2 >= ar_3 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)             evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)             evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)             evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.34/2.44	
5.34/2.44		start location:	koat_start
5.34/2.44	
5.34/2.44		leaf cost:	0
5.34/2.44	
5.34/2.44	
5.34/2.44	
5.34/2.44	A polynomial rank function with
5.34/2.44	
5.34/2.44		Pol(evalaxbb3in) = -V_2 + V_3
5.34/2.44	
5.34/2.44		Pol(evalaxbb2in) = -V_2 + V_3 + 1
5.34/2.44	
5.34/2.44	and size complexities
5.34/2.44	
5.34/2.44		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3))", 0-0) = 3*ar_2 + 2187
5.34/2.44	
5.34/2.44		S("evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3))", 0-3) = 3*ar_2 + 243
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ]", 0-0) = 3*ar_2 + 729
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ]", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ]", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ]", 0-3) = 3*ar_2 + 81
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]", 0-0) = 3*ar_2 + 729
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]", 0-3) = 3*ar_2 + 81
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\\ ar_2 >= ar_3 + 2 ]", 0-0) = 3*ar_2 + 27
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\\ ar_2 >= ar_3 + 2 ]", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\\ ar_2 >= ar_3 + 2 ]", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\\ ar_2 >= ar_3 + 2 ]", 0-3) = 3*ar_2 + 81
5.34/2.44	
5.34/2.44		S("evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))", 0-0) = 3*ar_2 + 243
5.34/2.44	
5.34/2.44		S("evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))", 0-3) = 3*ar_2 + 27
5.34/2.44	
5.34/2.44		S("evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))", 0-0) = 3*ar_2 + 81
5.34/2.44	
5.34/2.44		S("evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))", 0-3) = 3*ar_2 + 27
5.34/2.44	
5.34/2.44		S("evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))", 0-0) = 3*ar_2 + 27
5.34/2.44	
5.34/2.44		S("evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))", 0-3) = 3*ar_2 + 3*ar_3 + 729
5.34/2.44	
5.34/2.44		S("evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]", 0-0) = 3*ar_2 + 27
5.34/2.44	
5.34/2.44		S("evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]", 0-3) = 3*ar_2 + 3*ar_3 + 2187
5.34/2.44	
5.34/2.44		S("evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]", 0-0) = 3*ar_2 + 27
5.34/2.44	
5.34/2.44		S("evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]", 0-1) = ?
5.34/2.44	
5.34/2.44		S("evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]", 0-3) = 3*ar_2 + 3*ar_3 + 729
5.34/2.44	
5.34/2.44		S("evalaxbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, 0, ar_2, ar_3))", 0-0) = 3*ar_2 + 27
5.34/2.44	
5.34/2.44		S("evalaxbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, 0, ar_2, ar_3))", 0-1) = 0
5.34/2.44	
5.34/2.44		S("evalaxbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, 0, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalaxbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, 0, ar_2, ar_3))", 0-3) = 3*ar_2 + 3*ar_3 + 243
5.34/2.44	
5.34/2.44		S("evalax6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(0, ar_1, ar_2, ar_3))", 0-0) = 0
5.34/2.44	
5.34/2.44		S("evalax6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalax6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalax5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax6(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("evalax5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax6(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalax5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax6(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax6(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalax4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax5(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("evalax4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax5(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalax4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax5(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax5(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalax3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax4(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("evalax3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax4(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalax3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax4(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax4(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalax2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax3(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("evalax2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax3(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalax2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax3(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax3(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalax1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax2(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("evalax1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax2(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalax1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax2(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax2(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalax0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax1(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("evalax0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax1(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalax0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax1(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalax0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax1(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalaxbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax0(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("evalaxbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax0(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalaxbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax0(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalaxbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax0(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44		S("evalaxstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.34/2.44	
5.34/2.44		S("evalaxstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.34/2.44	
5.34/2.44		S("evalaxstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.34/2.44	
5.34/2.44		S("evalaxstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.34/2.44	
5.34/2.44	orients the transitions
5.34/2.44	
5.34/2.44		evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))
5.34/2.44	
5.34/2.44		evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44	weakly and the transition
5.34/2.44	
5.34/2.44		evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44	strictly and produces the following problem:
5.34/2.44	
5.34/2.44	7:	T:
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalaxstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalaxbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax0(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalax0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax1(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalax1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax2(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalax2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax3(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalax3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax4(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalax4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax5(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalax5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax6(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalax6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ar_2 + 1, Cost: 1)               evalaxbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, 0, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ar_2^2 + 2*ar_2 + 1, Cost: 1)    evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: 3*ar_2 + 3, Cost: 1)             evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44			(Comp: ?, Cost: 1)                      evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 3*ar_2 + 3, Cost: 1)             evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))
5.34/2.44	
5.34/2.44			(Comp: 3*ar_2 + 3, Cost: 1)             evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ar_2, Cost: 1)                   evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\ ar_2 >= ar_3 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)                      evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)                      evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)                      evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 0)                      koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.34/2.44	
5.34/2.44		start location:	koat_start
5.34/2.44	
5.34/2.44		leaf cost:	0
5.34/2.44	
5.34/2.44	
5.34/2.44	
5.34/2.44	Repeatedly propagating knowledge in problem 7 produces the following problem:
5.34/2.44	
5.34/2.44	8:	T:
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalaxstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalaxbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax0(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalax0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax1(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalax1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax2(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalax2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax3(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalax3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax4(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalax4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax5(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalax5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax6(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 1)                      evalax6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ar_2 + 1, Cost: 1)               evalaxbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, 0, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ar_2^2 + 2*ar_2 + 1, Cost: 1)    evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: 3*ar_2 + 3, Cost: 1)             evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44			(Comp: ar_2^2 + 2*ar_2 + 1, Cost: 1)    evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 3*ar_2 + 3, Cost: 1)             evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1))
5.34/2.44	
5.34/2.44			(Comp: 3*ar_2 + 3, Cost: 1)             evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: ar_2, Cost: 1)                   evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\ ar_2 >= ar_3 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)                      evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)                      evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ]
5.34/2.44	
5.34/2.44			(Comp: 2, Cost: 1)                      evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3))
5.34/2.44	
5.34/2.44			(Comp: 1, Cost: 0)                      koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.34/2.44	
5.34/2.44		start location:	koat_start
5.34/2.44	
5.34/2.44		leaf cost:	0
5.34/2.44	
5.34/2.44	
5.34/2.44	
5.34/2.44	Complexity upper bound 15*ar_2 + 2*ar_2^2 + 27
5.34/2.44	
5.34/2.44	
5.34/2.44	
5.34/2.44	Time: 0.204 sec (SMT: 0.151 sec)
5.34/2.44	
5.34/2.44	
5.34/2.44	----------------------------------------
5.34/2.44	
5.34/2.44	(2)
5.34/2.44	BOUNDS(1, n^2)
5.34/2.44	
5.34/2.44	----------------------------------------
5.34/2.44	
5.34/2.44	(3) Loat Proof (FINISHED)
5.34/2.44	
5.34/2.44	
5.34/2.44	### Pre-processing the ITS problem ###
5.34/2.44	
5.34/2.44	
5.34/2.44	
5.34/2.44	Initial linear ITS problem
5.34/2.44	
5.34/2.44	   Start location: evalaxstart
5.34/2.44	
5.34/2.44	      0: evalaxstart -> evalaxbb0in : [], cost: 1
5.34/2.44	
5.34/2.44	      1: evalaxbb0in -> evalax0 : [], cost: 1
5.34/2.44	
5.34/2.44	      2: evalax0 -> evalax1 : [], cost: 1
5.34/2.44	
5.34/2.44	      3: evalax1 -> evalax2 : [], cost: 1
5.34/2.44	
5.34/2.44	      4: evalax2 -> evalax3 : [], cost: 1
5.34/2.44	
5.34/2.44	      5: evalax3 -> evalax4 : [], cost: 1
5.34/2.44	
5.34/2.44	      6: evalax4 -> evalax5 : [], cost: 1
5.34/2.44	
5.34/2.44	      7: evalax5 -> evalax6 : [], cost: 1
5.34/2.44	
5.34/2.44	      8: evalax6 -> evalaxbb1in : A'=0, [], cost: 1
5.34/2.44	
5.34/2.44	      9: evalaxbb1in -> evalaxbb2in : B'=0, [], cost: 1
5.34/2.44	
5.34/2.44	     10: evalaxbb2in -> evalaxbb3in : [ C>=2+B ], cost: 1
5.34/2.44	
5.34/2.44	     11: evalaxbb2in -> evalaxbb4in : [ 1+B>=C ], cost: 1
5.34/2.44	
5.34/2.44	     12: evalaxbb3in -> evalaxbb2in : B'=1+B, [], cost: 1
5.34/2.44	
5.34/2.44	     13: evalaxbb4in -> evalax12 : D'=1+A, [], cost: 1
5.34/2.44	
5.34/2.44	     14: evalax12 -> evalax13 : [], cost: 1
5.34/2.45	
5.34/2.45	     15: evalax13 -> evalaxbb1in : A'=D, [ 1+B>=C && C>=2+D ], cost: 1
5.34/2.45	
5.34/2.45	     16: evalax13 -> evalaxbb5in : [ C>=2+B ], cost: 1
5.34/2.45	
5.34/2.45	     17: evalax13 -> evalaxbb5in : [ 1+D>=C ], cost: 1
5.34/2.45	
5.34/2.45	     18: evalaxbb5in -> evalaxstop : [], cost: 1
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	Removed unreachable and leaf rules:
5.34/2.45	
5.34/2.45	   Start location: evalaxstart
5.34/2.45	
5.34/2.45	      0: evalaxstart -> evalaxbb0in : [], cost: 1
5.34/2.45	
5.34/2.45	      1: evalaxbb0in -> evalax0 : [], cost: 1
5.34/2.45	
5.34/2.45	      2: evalax0 -> evalax1 : [], cost: 1
5.34/2.45	
5.34/2.45	      3: evalax1 -> evalax2 : [], cost: 1
5.34/2.45	
5.34/2.45	      4: evalax2 -> evalax3 : [], cost: 1
5.34/2.45	
5.34/2.45	      5: evalax3 -> evalax4 : [], cost: 1
5.34/2.45	
5.34/2.45	      6: evalax4 -> evalax5 : [], cost: 1
5.34/2.45	
5.34/2.45	      7: evalax5 -> evalax6 : [], cost: 1
5.34/2.45	
5.34/2.45	      8: evalax6 -> evalaxbb1in : A'=0, [], cost: 1
5.34/2.45	
5.34/2.45	      9: evalaxbb1in -> evalaxbb2in : B'=0, [], cost: 1
5.34/2.45	
5.34/2.45	     10: evalaxbb2in -> evalaxbb3in : [ C>=2+B ], cost: 1
5.34/2.45	
5.34/2.45	     11: evalaxbb2in -> evalaxbb4in : [ 1+B>=C ], cost: 1
5.34/2.45	
5.34/2.45	     12: evalaxbb3in -> evalaxbb2in : B'=1+B, [], cost: 1
5.34/2.45	
5.34/2.45	     13: evalaxbb4in -> evalax12 : D'=1+A, [], cost: 1
5.34/2.45	
5.34/2.45	     14: evalax12 -> evalax13 : [], cost: 1
5.34/2.45	
5.34/2.45	     15: evalax13 -> evalaxbb1in : A'=D, [ 1+B>=C && C>=2+D ], cost: 1
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	### Simplification by acceleration and chaining ###
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5.34/2.45	
5.34/2.45	
5.34/2.45	Eliminated locations (on linear paths):
5.34/2.45	
5.34/2.45	   Start location: evalaxstart
5.34/2.45	
5.34/2.45	     26: evalaxstart -> evalaxbb1in : A'=0, [], cost: 9
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5.34/2.45	      9: evalaxbb1in -> evalaxbb2in : B'=0, [], cost: 1
5.34/2.45	
5.34/2.45	     27: evalaxbb2in -> evalaxbb2in : B'=1+B, [ C>=2+B ], cost: 2
5.34/2.45	
5.34/2.45	     30: evalaxbb2in -> evalaxbb1in : A'=1+A, D'=1+A, [ 1+B>=C && C>=3+A ], cost: 4
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	Accelerating simple loops of location 10.
5.34/2.45	
5.34/2.45	   Accelerating the following rules:
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5.34/2.45	     27: evalaxbb2in -> evalaxbb2in : B'=1+B, [ C>=2+B ], cost: 2
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	   Accelerated rule 27 with metering function -1+C-B, yielding the new rule 31.
5.34/2.45	
5.34/2.45	   Removing the simple loops: 27.
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	Accelerated all simple loops using metering functions (where possible):
5.34/2.45	
5.34/2.45	   Start location: evalaxstart
5.34/2.45	
5.34/2.45	     26: evalaxstart -> evalaxbb1in : A'=0, [], cost: 9
5.34/2.45	
5.34/2.45	      9: evalaxbb1in -> evalaxbb2in : B'=0, [], cost: 1
5.34/2.45	
5.34/2.45	     30: evalaxbb2in -> evalaxbb1in : A'=1+A, D'=1+A, [ 1+B>=C && C>=3+A ], cost: 4
5.34/2.45	
5.34/2.45	     31: evalaxbb2in -> evalaxbb2in : B'=-1+C, [ C>=2+B ], cost: -2+2*C-2*B
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	Chained accelerated rules (with incoming rules):
5.34/2.45	
5.34/2.45	   Start location: evalaxstart
5.34/2.45	
5.34/2.45	     26: evalaxstart -> evalaxbb1in : A'=0, [], cost: 9
5.34/2.45	
5.34/2.45	      9: evalaxbb1in -> evalaxbb2in : B'=0, [], cost: 1
5.34/2.45	
5.34/2.45	     32: evalaxbb1in -> evalaxbb2in : B'=-1+C, [ C>=2 ], cost: -1+2*C
5.34/2.45	
5.34/2.45	     30: evalaxbb2in -> evalaxbb1in : A'=1+A, D'=1+A, [ 1+B>=C && C>=3+A ], cost: 4
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	Eliminated locations (on tree-shaped paths):
5.34/2.45	
5.34/2.45	   Start location: evalaxstart
5.34/2.45	
5.34/2.45	     26: evalaxstart -> evalaxbb1in : A'=0, [], cost: 9
5.34/2.45	
5.34/2.45	     33: evalaxbb1in -> evalaxbb1in : A'=1+A, B'=0, D'=1+A, [ 1>=C && C>=3+A ], cost: 5
5.34/2.45	
5.34/2.45	     34: evalaxbb1in -> evalaxbb1in : A'=1+A, B'=-1+C, D'=1+A, [ C>=2 && C>=3+A ], cost: 3+2*C
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	Accelerating simple loops of location 9.
5.34/2.45	
5.34/2.45	   Accelerating the following rules:
5.34/2.45	
5.34/2.45	     33: evalaxbb1in -> evalaxbb1in : A'=1+A, B'=0, D'=1+A, [ 1>=C && C>=3+A ], cost: 5
5.34/2.45	
5.34/2.45	     34: evalaxbb1in -> evalaxbb1in : A'=1+A, B'=-1+C, D'=1+A, [ C>=2 && C>=3+A ], cost: 3+2*C
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	   Accelerated rule 33 with metering function -2+C-A, yielding the new rule 35.
5.34/2.45	
5.34/2.45	   Accelerated rule 34 with metering function -2+C-A, yielding the new rule 36.
5.34/2.45	
5.34/2.45	   Removing the simple loops: 33 34.
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	Accelerated all simple loops using metering functions (where possible):
5.34/2.45	
5.34/2.45	   Start location: evalaxstart
5.34/2.45	
5.34/2.45	     26: evalaxstart -> evalaxbb1in : A'=0, [], cost: 9
5.34/2.45	
5.34/2.45	     35: evalaxbb1in -> evalaxbb1in : A'=-2+C, B'=0, D'=-2+C, [ 1>=C && C>=3+A ], cost: -10+5*C-5*A
5.34/2.45	
5.34/2.45	     36: evalaxbb1in -> evalaxbb1in : A'=-2+C, B'=-1+C, D'=-2+C, [ C>=2 && C>=3+A ], cost: -6+3*C+2*C*(-2+C-A)-3*A
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	Chained accelerated rules (with incoming rules):
5.34/2.45	
5.34/2.45	   Start location: evalaxstart
5.34/2.45	
5.34/2.45	     26: evalaxstart -> evalaxbb1in : A'=0, [], cost: 9
5.34/2.45	
5.34/2.45	     37: evalaxstart -> evalaxbb1in : A'=-2+C, B'=-1+C, D'=-2+C, [ C>=3 ], cost: 3+2*(-2+C)*C+3*C
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	Removed unreachable locations (and leaf rules with constant cost):
5.34/2.45	
5.34/2.45	   Start location: evalaxstart
5.34/2.45	
5.34/2.45	     37: evalaxstart -> evalaxbb1in : A'=-2+C, B'=-1+C, D'=-2+C, [ C>=3 ], cost: 3+2*(-2+C)*C+3*C
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	### Computing asymptotic complexity ###
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	Fully simplified ITS problem
5.34/2.45	
5.34/2.45	   Start location: evalaxstart
5.34/2.45	
5.34/2.45	     37: evalaxstart -> evalaxbb1in : A'=-2+C, B'=-1+C, D'=-2+C, [ C>=3 ], cost: 3+2*(-2+C)*C+3*C
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	Computing asymptotic complexity for rule 37
5.34/2.45	
5.34/2.45	   Solved the limit problem by the following transformations:
5.34/2.45	
5.34/2.45	      Created initial limit problem:
5.34/2.45	
5.34/2.45	      -2+C (+/+!), 3+2*C^2-C (+) [not solved]
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	      removing all constraints (solved by SMT)
5.34/2.45	
5.34/2.45	      resulting limit problem: [solved]
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	      applying transformation rule (C) using substitution {C==n}
5.34/2.45	
5.34/2.45	      resulting limit problem:
5.34/2.45	
5.34/2.45	      [solved]
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	   Solution:
5.34/2.45	
5.34/2.45	      C / n
5.34/2.45	
5.34/2.45	   Resulting cost 3-n+2*n^2 has complexity: Poly(n^2)
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	Found new complexity Poly(n^2).
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	Obtained the following overall complexity (w.r.t. the length of the input n):
5.34/2.45	
5.34/2.45	   Complexity:  Poly(n^2)
5.34/2.45	
5.34/2.45	   Cpx degree:  2
5.34/2.45	
5.34/2.45	   Solved cost: 3-n+2*n^2
5.34/2.45	
5.34/2.45	   Rule cost:   3+2*(-2+C)*C+3*C
5.34/2.45	
5.34/2.45	   Rule guard:  [ C>=3 ]
5.34/2.45	
5.34/2.45	
5.34/2.45	
5.34/2.45	WORST_CASE(Omega(n^2),?)
5.34/2.45	
5.34/2.45	
5.34/2.45	----------------------------------------
5.34/2.45	
5.34/2.45	(4)
5.34/2.45	BOUNDS(n^2, INF)
5.34/2.46	EOF