15.33/9.33	WORST_CASE(Omega(n^1), O(n^1))
15.33/9.34	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
15.33/9.34	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
15.33/9.34	
15.33/9.34	
15.33/9.34	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, nat(2 + 6 * Arg_2 + -6 * Arg_4) + nat(3 + 3 * Arg_2 + -3 * Arg_4) + max(6 + Arg_2 + -1 * Arg_4, 5) + max(4, 5 + 2 * Arg_2 + -2 * Arg_4)).
15.33/9.34	
15.33/9.34	(0) CpxIntTrs
15.33/9.34	(1) Koat2 Proof [FINISHED, 3739 ms]
15.33/9.34	(2) BOUNDS(1, nat(2 + 6 * Arg_2 + -6 * Arg_4) + nat(3 + 3 * Arg_2 + -3 * Arg_4) + max(6 + Arg_2 + -1 * Arg_4, 5) + max(4, 5 + 2 * Arg_2 + -2 * Arg_4))
15.33/9.34	(3) Loat Proof [FINISHED, 7570 ms]
15.33/9.34	(4) BOUNDS(n^1, INF)
15.33/9.34	
15.33/9.34	
15.33/9.34	----------------------------------------
15.33/9.34	
15.33/9.34	(0)
15.33/9.34	Obligation:
15.33/9.34	Complexity Int TRS consisting of the following rules:
15.33/9.34	eval_aaron2_start(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb0_in(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: TRUE
15.33/9.34	eval_aaron2_bb0_in(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_0(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: TRUE
15.33/9.34	eval_aaron2_0(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_1(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: TRUE
15.33/9.34	eval_aaron2_1(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_2(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: TRUE
15.33/9.34	eval_aaron2_2(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_3(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: TRUE
15.33/9.34	eval_aaron2_3(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb1_in(v_x, v_y, v_3, v_tx, v_x, v_y)) :|: v_tx >= 0
15.33/9.34	eval_aaron2_3(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb5_in(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: v_tx < 0
15.33/9.34	eval_aaron2_bb1_in(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb5_in(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: v__01 < v__02
15.33/9.34	eval_aaron2_bb1_in(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb5_in(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: v_tx < 0
15.33/9.34	eval_aaron2_bb1_in(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb2_in(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: v__01 >= v__02 && v_tx >= 0
15.33/9.34	eval_aaron2_bb2_in(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_4(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: TRUE
15.33/9.34	eval_aaron2_4(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_5(v__01, v__02, nondef_0, v_tx, v_x, v_y)) :|: TRUE
15.33/9.34	eval_aaron2_5(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb3_in(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: v_3 > 0
15.33/9.34	eval_aaron2_5(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb4_in(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: v_3 <= 0
15.33/9.34	eval_aaron2_bb3_in(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb1_in(v__01 - v_tx - 1, v__02, v_3, v_tx, v_x, v_y)) :|: TRUE
15.33/9.34	eval_aaron2_bb4_in(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb1_in(v__01, v__02 + v_tx + 1, v_3, v_tx, v_x, v_y)) :|: TRUE
15.33/9.34	eval_aaron2_bb5_in(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_stop(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: TRUE
15.33/9.34	
15.33/9.34	The start-symbols are:[eval_aaron2_start_6]
15.33/9.34	
15.33/9.34	
15.33/9.34	----------------------------------------
15.33/9.34	
15.33/9.34	(1) Koat2 Proof (FINISHED)
15.33/9.34	YES( ?, 4+max([0, 1+2*Arg_2+-2*Arg_4])+max([0, 1+3*Arg_2+-3*Arg_4])+max([0, 1+3*Arg_2+-3*Arg_4])+max([0, 1+Arg_2-Arg_4])+max([0, 1+Arg_2-Arg_4])+max([5, 6+Arg_2-Arg_4])+max([0, 1+Arg_2-Arg_4]) {O(n)})
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	Initial Complexity Problem:
15.33/9.34	
15.33/9.34	  Start:  evalaaron2start  
15.33/9.34	
15.33/9.34	  Program_Vars:  Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5  
15.33/9.34	
15.33/9.34	  Temp_Vars:  G  
15.33/9.34	
15.33/9.34	  Locations:  evalaaron20, evalaaron21, evalaaron22, evalaaron23, evalaaron24, evalaaron25, evalaaron2bb0in, evalaaron2bb1in, evalaaron2bb2in, evalaaron2bb3in, evalaaron2bb4in, evalaaron2bb5in, evalaaron2start, evalaaron2stop  
15.33/9.34	
15.33/9.34	  Transitions:
15.33/9.34	
15.33/9.34	  evalaaron20(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron21(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:
15.33/9.34	
15.33/9.34	  evalaaron21(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron22(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:
15.33/9.34	
15.33/9.34	  evalaaron22(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron23(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:
15.33/9.34	
15.33/9.34	  evalaaron23(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb1in(Arg_0,Arg_2,Arg_2,Arg_4,Arg_4,Arg_5):|:0 <= Arg_0
15.33/9.34	
15.33/9.34	  evalaaron23(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0+1 <= 0
15.33/9.34	
15.33/9.34	  evalaaron24(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,G):|:Arg_4 <= Arg_3 && Arg_4 <= Arg_2 && Arg_4 <= Arg_1 && Arg_3 <= Arg_2 && Arg_3 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0
15.33/9.34	
15.33/9.34	  evalaaron25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_4 <= Arg_3 && Arg_4 <= Arg_2 && Arg_4 <= Arg_1 && Arg_3 <= Arg_2 && Arg_3 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 && 1 <= Arg_5
15.33/9.34	
15.33/9.34	  evalaaron25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_4 <= Arg_3 && Arg_4 <= Arg_2 && Arg_4 <= Arg_1 && Arg_3 <= Arg_2 && Arg_3 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 && Arg_5 <= 0
15.33/9.34	
15.33/9.34	  evalaaron2bb0in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron20(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:
15.33/9.34	
15.33/9.34	  evalaaron2bb1in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_4 <= Arg_3 && Arg_1 <= Arg_2 && 0 <= Arg_0 && Arg_3 <= Arg_1 && 0 <= Arg_0
15.33/9.34	
15.33/9.34	  evalaaron2bb1in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_4 <= Arg_3 && Arg_1 <= Arg_2 && 0 <= Arg_0 && Arg_1+1 <= Arg_3
15.33/9.34	
15.33/9.34	  evalaaron2bb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron24(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_4 <= Arg_3 && Arg_4 <= Arg_2 && Arg_4 <= Arg_1 && Arg_3 <= Arg_2 && Arg_3 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0
15.33/9.34	
15.33/9.34	  evalaaron2bb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb1in(Arg_0,Arg_1-Arg_0-1,Arg_2,Arg_3,Arg_4,Arg_5):|:1 <= Arg_5 && 1 <= Arg_0+Arg_5 && Arg_4 <= Arg_3 && Arg_4 <= Arg_2 && Arg_4 <= Arg_1 && Arg_3 <= Arg_2 && Arg_3 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0
15.33/9.34	
15.33/9.34	  evalaaron2bb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb1in(Arg_0,Arg_1,Arg_2,Arg_3+Arg_0+1,Arg_4,Arg_5):|:Arg_5 <= 0 && Arg_5 <= Arg_0 && Arg_4 <= Arg_3 && Arg_4 <= Arg_2 && Arg_4 <= Arg_1 && Arg_3 <= Arg_2 && Arg_3 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0
15.33/9.34	
15.33/9.34	  evalaaron2bb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:
15.33/9.34	
15.33/9.34	  evalaaron2start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb0in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:  
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	Timebounds: 
15.33/9.34	
15.33/9.34	  Overall timebound: 4+max([0, 1+2*Arg_2+-2*Arg_4])+max([0, 1+3*Arg_2+-3*Arg_4])+max([0, 1+3*Arg_2+-3*Arg_4])+max([0, 1+Arg_2-Arg_4])+max([0, 1+Arg_2-Arg_4])+max([5, 6+Arg_2-Arg_4])+max([0, 1+Arg_2-Arg_4]) {O(n)}
15.33/9.34	
15.33/9.34	  2: evalaaron20->evalaaron21: 1 {O(1)}
15.33/9.34	
15.33/9.34	  3: evalaaron21->evalaaron22: 1 {O(1)}
15.33/9.34	
15.33/9.34	  4: evalaaron22->evalaaron23: 1 {O(1)}
15.33/9.34	
15.33/9.34	  5: evalaaron23->evalaaron2bb1in: 1 {O(1)}
15.33/9.34	
15.33/9.34	  6: evalaaron23->evalaaron2bb5in: 1 {O(1)}
15.33/9.34	
15.33/9.34	  11: evalaaron24->evalaaron25: max([0, 1+Arg_2-Arg_4]) {O(n)}
15.33/9.34	
15.33/9.34	  12: evalaaron25->evalaaron2bb3in: max([0, 1+Arg_2-Arg_4]) {O(n)}
15.33/9.34	
15.33/9.34	  13: evalaaron25->evalaaron2bb4in: max([0, 1+3*Arg_2+-3*Arg_4]) {O(n)}
15.33/9.34	
15.33/9.34	  1: evalaaron2bb0in->evalaaron20: 1 {O(1)}
15.33/9.34	
15.33/9.34	  7: evalaaron2bb1in->evalaaron2bb5in: 1 {O(1)}
15.33/9.34	
15.33/9.34	  9: evalaaron2bb1in->evalaaron2bb2in: max([0, 1+Arg_2-Arg_4]) {O(n)}
15.33/9.34	
15.33/9.34	  10: evalaaron2bb2in->evalaaron24: max([0, 1+Arg_2-Arg_4]) {O(n)}
15.33/9.34	
15.33/9.34	  14: evalaaron2bb3in->evalaaron2bb1in: max([0, 1+3*Arg_2+-3*Arg_4]) {O(n)}
15.33/9.34	
15.33/9.34	  15: evalaaron2bb4in->evalaaron2bb1in: max([0, 1+2*Arg_2+-2*Arg_4]) {O(n)}
15.33/9.34	
15.33/9.34	  16: evalaaron2bb5in->evalaaron2stop: 1 {O(1)}
15.33/9.34	
15.33/9.34	  0: evalaaron2start->evalaaron2bb0in: 1 {O(1)}
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	Costbounds:
15.33/9.34	
15.33/9.34	  Overall costbound: 4+max([0, 1+2*Arg_2+-2*Arg_4])+max([0, 1+3*Arg_2+-3*Arg_4])+max([0, 1+3*Arg_2+-3*Arg_4])+max([0, 1+Arg_2-Arg_4])+max([0, 1+Arg_2-Arg_4])+max([5, 6+Arg_2-Arg_4])+max([0, 1+Arg_2-Arg_4]) {O(n)}
15.33/9.34	
15.33/9.34	  2: evalaaron20->evalaaron21: 1 {O(1)}
15.33/9.34	
15.33/9.34	  3: evalaaron21->evalaaron22: 1 {O(1)}
15.33/9.34	
15.33/9.34	  4: evalaaron22->evalaaron23: 1 {O(1)}
15.33/9.34	
15.33/9.34	  5: evalaaron23->evalaaron2bb1in: 1 {O(1)}
15.33/9.34	
15.33/9.34	  6: evalaaron23->evalaaron2bb5in: 1 {O(1)}
15.33/9.34	
15.33/9.34	  11: evalaaron24->evalaaron25: max([0, 1+Arg_2-Arg_4]) {O(n)}
15.33/9.34	
15.33/9.34	  12: evalaaron25->evalaaron2bb3in: max([0, 1+Arg_2-Arg_4]) {O(n)}
15.33/9.34	
15.33/9.34	  13: evalaaron25->evalaaron2bb4in: max([0, 1+3*Arg_2+-3*Arg_4]) {O(n)}
15.33/9.34	
15.33/9.34	  1: evalaaron2bb0in->evalaaron20: 1 {O(1)}
15.33/9.34	
15.33/9.34	  7: evalaaron2bb1in->evalaaron2bb5in: 1 {O(1)}
15.33/9.34	
15.33/9.34	  9: evalaaron2bb1in->evalaaron2bb2in: max([0, 1+Arg_2-Arg_4]) {O(n)}
15.33/9.34	
15.33/9.34	  10: evalaaron2bb2in->evalaaron24: max([0, 1+Arg_2-Arg_4]) {O(n)}
15.33/9.34	
15.33/9.34	  14: evalaaron2bb3in->evalaaron2bb1in: max([0, 1+3*Arg_2+-3*Arg_4]) {O(n)}
15.33/9.34	
15.33/9.34	  15: evalaaron2bb4in->evalaaron2bb1in: max([0, 1+2*Arg_2+-2*Arg_4]) {O(n)}
15.33/9.34	
15.33/9.34	  16: evalaaron2bb5in->evalaaron2stop: 1 {O(1)}
15.33/9.34	
15.33/9.34	  0: evalaaron2start->evalaaron2bb0in: 1 {O(1)}
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	Sizebounds:
15.33/9.34	
15.33/9.34	`Lower:
15.33/9.34	
15.33/9.34	  2: evalaaron20->evalaaron21, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  2: evalaaron20->evalaaron21, Arg_1: Arg_1 {O(n)}
15.33/9.34	
15.33/9.34	  2: evalaaron20->evalaaron21, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  2: evalaaron20->evalaaron21, Arg_3: Arg_3 {O(n)}
15.33/9.34	
15.33/9.34	  2: evalaaron20->evalaaron21, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  2: evalaaron20->evalaaron21, Arg_5: Arg_5 {O(n)}
15.33/9.34	
15.33/9.34	  3: evalaaron21->evalaaron22, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  3: evalaaron21->evalaaron22, Arg_1: Arg_1 {O(n)}
15.33/9.34	
15.33/9.34	  3: evalaaron21->evalaaron22, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  3: evalaaron21->evalaaron22, Arg_3: Arg_3 {O(n)}
15.33/9.34	
15.33/9.34	  3: evalaaron21->evalaaron22, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  3: evalaaron21->evalaaron22, Arg_5: Arg_5 {O(n)}
15.33/9.34	
15.33/9.34	  4: evalaaron22->evalaaron23, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  4: evalaaron22->evalaaron23, Arg_1: Arg_1 {O(n)}
15.33/9.34	
15.33/9.34	  4: evalaaron22->evalaaron23, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  4: evalaaron22->evalaaron23, Arg_3: Arg_3 {O(n)}
15.33/9.34	
15.33/9.34	  4: evalaaron22->evalaaron23, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  4: evalaaron22->evalaaron23, Arg_5: Arg_5 {O(n)}
15.33/9.34	
15.33/9.34	  5: evalaaron23->evalaaron2bb1in, Arg_0: 0 {O(1)}
15.33/9.34	
15.33/9.34	  5: evalaaron23->evalaaron2bb1in, Arg_1: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  5: evalaaron23->evalaaron2bb1in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  5: evalaaron23->evalaaron2bb1in, Arg_3: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  5: evalaaron23->evalaaron2bb1in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  5: evalaaron23->evalaaron2bb1in, Arg_5: Arg_5 {O(n)}
15.33/9.34	
15.33/9.34	  6: evalaaron23->evalaaron2bb5in, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  6: evalaaron23->evalaaron2bb5in, Arg_1: Arg_1 {O(n)}
15.33/9.34	
15.33/9.34	  6: evalaaron23->evalaaron2bb5in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  6: evalaaron23->evalaaron2bb5in, Arg_3: Arg_3 {O(n)}
15.33/9.34	
15.33/9.34	  6: evalaaron23->evalaaron2bb5in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  6: evalaaron23->evalaaron2bb5in, Arg_5: Arg_5 {O(n)}
15.33/9.34	
15.33/9.34	  11: evalaaron24->evalaaron25, Arg_0: 0 {O(1)}
15.33/9.34	
15.33/9.34	  11: evalaaron24->evalaaron25, Arg_1: min([0, Arg_2])-max([0, (1+3*Arg_2+-3*Arg_4)*max([1, 1+Arg_0])]) {O(n^2)}
15.33/9.34	
15.33/9.34	  11: evalaaron24->evalaaron25, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  11: evalaaron24->evalaaron25, Arg_3: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  11: evalaaron24->evalaaron25, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  12: evalaaron25->evalaaron2bb3in, Arg_0: 0 {O(1)}
15.33/9.34	
15.33/9.34	  12: evalaaron25->evalaaron2bb3in, Arg_1: min([0, Arg_2])-max([0, (1+3*Arg_2+-3*Arg_4)*max([1, 1+Arg_0])]) {O(n^2)}
15.33/9.34	
15.33/9.34	  12: evalaaron25->evalaaron2bb3in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  12: evalaaron25->evalaaron2bb3in, Arg_3: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  12: evalaaron25->evalaaron2bb3in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  12: evalaaron25->evalaaron2bb3in, Arg_5: 1 {O(1)}
15.33/9.34	
15.33/9.34	  13: evalaaron25->evalaaron2bb4in, Arg_0: 0 {O(1)}
15.33/9.34	
15.33/9.34	  13: evalaaron25->evalaaron2bb4in, Arg_1: min([0, Arg_2])-max([0, (1+3*Arg_2+-3*Arg_4)*max([1, 1+Arg_0])]) {O(n^2)}
15.33/9.34	
15.33/9.34	  13: evalaaron25->evalaaron2bb4in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  13: evalaaron25->evalaaron2bb4in, Arg_3: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  13: evalaaron25->evalaaron2bb4in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  1: evalaaron2bb0in->evalaaron20, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  1: evalaaron2bb0in->evalaaron20, Arg_1: Arg_1 {O(n)}
15.33/9.34	
15.33/9.34	  1: evalaaron2bb0in->evalaaron20, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  1: evalaaron2bb0in->evalaaron20, Arg_3: Arg_3 {O(n)}
15.33/9.34	
15.33/9.34	  1: evalaaron2bb0in->evalaaron20, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  1: evalaaron2bb0in->evalaaron20, Arg_5: Arg_5 {O(n)}
15.33/9.34	
15.33/9.34	  7: evalaaron2bb1in->evalaaron2bb5in, Arg_0: 0 {O(1)}
15.33/9.34	
15.33/9.34	  7: evalaaron2bb1in->evalaaron2bb5in, Arg_1: min([Arg_2, -(max([0, -(Arg_2)])+max([0, (1+3*Arg_2+-3*Arg_4)*max([1, 1+Arg_0])]))]) {O(n^2)}
15.33/9.34	
15.33/9.34	  7: evalaaron2bb1in->evalaaron2bb5in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  7: evalaaron2bb1in->evalaaron2bb5in, Arg_3: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  7: evalaaron2bb1in->evalaaron2bb5in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  9: evalaaron2bb1in->evalaaron2bb2in, Arg_0: 0 {O(1)}
15.33/9.34	
15.33/9.34	  9: evalaaron2bb1in->evalaaron2bb2in, Arg_1: min([0, Arg_2])-max([0, (1+3*Arg_2+-3*Arg_4)*max([1, 1+Arg_0])]) {O(n^2)}
15.33/9.34	
15.33/9.34	  9: evalaaron2bb1in->evalaaron2bb2in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  9: evalaaron2bb1in->evalaaron2bb2in, Arg_3: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  9: evalaaron2bb1in->evalaaron2bb2in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  10: evalaaron2bb2in->evalaaron24, Arg_0: 0 {O(1)}
15.33/9.34	
15.33/9.34	  10: evalaaron2bb2in->evalaaron24, Arg_1: min([0, Arg_2])-max([0, (1+3*Arg_2+-3*Arg_4)*max([1, 1+Arg_0])]) {O(n^2)}
15.33/9.34	
15.33/9.34	  10: evalaaron2bb2in->evalaaron24, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  10: evalaaron2bb2in->evalaaron24, Arg_3: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  10: evalaaron2bb2in->evalaaron24, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  14: evalaaron2bb3in->evalaaron2bb1in, Arg_0: 0 {O(1)}
15.33/9.34	
15.33/9.34	  14: evalaaron2bb3in->evalaaron2bb1in, Arg_1: min([0, Arg_2])-max([0, (1+3*Arg_2+-3*Arg_4)*max([1, 1+Arg_0])]) {O(n^2)}
15.33/9.34	
15.33/9.34	  14: evalaaron2bb3in->evalaaron2bb1in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  14: evalaaron2bb3in->evalaaron2bb1in, Arg_3: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  14: evalaaron2bb3in->evalaaron2bb1in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  14: evalaaron2bb3in->evalaaron2bb1in, Arg_5: 1 {O(1)}
15.33/9.34	
15.33/9.34	  15: evalaaron2bb4in->evalaaron2bb1in, Arg_0: 0 {O(1)}
15.33/9.34	
15.33/9.34	  15: evalaaron2bb4in->evalaaron2bb1in, Arg_1: min([0, Arg_2])-max([0, (1+3*Arg_2+-3*Arg_4)*max([1, 1+Arg_0])]) {O(n^2)}
15.33/9.34	
15.33/9.34	  15: evalaaron2bb4in->evalaaron2bb1in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  15: evalaaron2bb4in->evalaaron2bb1in, Arg_3: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  15: evalaaron2bb4in->evalaaron2bb1in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  16: evalaaron2bb5in->evalaaron2stop, Arg_0: min([0, Arg_0]) {O(n)}
15.33/9.34	
15.33/9.34	  16: evalaaron2bb5in->evalaaron2stop, Arg_1: min([Arg_2, min([Arg_1, -(max([0, -(Arg_2)])+max([0, (1+3*Arg_2+-3*Arg_4)*max([1, 1+Arg_0])]))])]) {O(n^2)}
15.33/9.34	
15.33/9.34	  16: evalaaron2bb5in->evalaaron2stop, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  16: evalaaron2bb5in->evalaaron2stop, Arg_3: min([Arg_4, Arg_3]) {O(n)}
15.33/9.34	
15.33/9.34	  16: evalaaron2bb5in->evalaaron2stop, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  0: evalaaron2start->evalaaron2bb0in, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  0: evalaaron2start->evalaaron2bb0in, Arg_1: Arg_1 {O(n)}
15.33/9.34	
15.33/9.34	  0: evalaaron2start->evalaaron2bb0in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  0: evalaaron2start->evalaaron2bb0in, Arg_3: Arg_3 {O(n)}
15.33/9.34	
15.33/9.34	  0: evalaaron2start->evalaaron2bb0in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  0: evalaaron2start->evalaaron2bb0in, Arg_5: Arg_5 {O(n)}
15.33/9.34	
15.33/9.34	`Upper:
15.33/9.34	
15.33/9.34	  2: evalaaron20->evalaaron21, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  2: evalaaron20->evalaaron21, Arg_1: Arg_1 {O(n)}
15.33/9.34	
15.33/9.34	  2: evalaaron20->evalaaron21, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  2: evalaaron20->evalaaron21, Arg_3: Arg_3 {O(n)}
15.33/9.34	
15.33/9.34	  2: evalaaron20->evalaaron21, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  2: evalaaron20->evalaaron21, Arg_5: Arg_5 {O(n)}
15.33/9.34	
15.33/9.34	  3: evalaaron21->evalaaron22, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  3: evalaaron21->evalaaron22, Arg_1: Arg_1 {O(n)}
15.33/9.34	
15.33/9.34	  3: evalaaron21->evalaaron22, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  3: evalaaron21->evalaaron22, Arg_3: Arg_3 {O(n)}
15.33/9.34	
15.33/9.34	  3: evalaaron21->evalaaron22, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  3: evalaaron21->evalaaron22, Arg_5: Arg_5 {O(n)}
15.33/9.34	
15.33/9.34	  4: evalaaron22->evalaaron23, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  4: evalaaron22->evalaaron23, Arg_1: Arg_1 {O(n)}
15.33/9.34	
15.33/9.34	  4: evalaaron22->evalaaron23, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  4: evalaaron22->evalaaron23, Arg_3: Arg_3 {O(n)}
15.33/9.34	
15.33/9.34	  4: evalaaron22->evalaaron23, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  4: evalaaron22->evalaaron23, Arg_5: Arg_5 {O(n)}
15.33/9.34	
15.33/9.34	  5: evalaaron23->evalaaron2bb1in, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  5: evalaaron23->evalaaron2bb1in, Arg_1: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  5: evalaaron23->evalaaron2bb1in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  5: evalaaron23->evalaaron2bb1in, Arg_3: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  5: evalaaron23->evalaaron2bb1in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  5: evalaaron23->evalaaron2bb1in, Arg_5: Arg_5 {O(n)}
15.33/9.34	
15.33/9.34	  6: evalaaron23->evalaaron2bb5in, Arg_0: -1 {O(1)}
15.33/9.34	
15.33/9.34	  6: evalaaron23->evalaaron2bb5in, Arg_1: Arg_1 {O(n)}
15.33/9.34	
15.33/9.34	  6: evalaaron23->evalaaron2bb5in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  6: evalaaron23->evalaaron2bb5in, Arg_3: Arg_3 {O(n)}
15.33/9.34	
15.33/9.34	  6: evalaaron23->evalaaron2bb5in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  6: evalaaron23->evalaaron2bb5in, Arg_5: Arg_5 {O(n)}
15.33/9.34	
15.33/9.34	  11: evalaaron24->evalaaron25, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  11: evalaaron24->evalaaron25, Arg_1: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  11: evalaaron24->evalaaron25, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  11: evalaaron24->evalaaron25, Arg_3: max([Arg_0, Arg_4])+max([0, (1+2*Arg_2+-2*Arg_4)*max([1, 1+Arg_0])]) {O(n^2)}
15.33/9.34	
15.33/9.34	  11: evalaaron24->evalaaron25, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  12: evalaaron25->evalaaron2bb3in, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  12: evalaaron25->evalaaron2bb3in, Arg_1: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  12: evalaaron25->evalaaron2bb3in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  12: evalaaron25->evalaaron2bb3in, Arg_3: max([Arg_0, Arg_4])+max([0, (1+2*Arg_2+-2*Arg_4)*max([1, 1+Arg_0])]) {O(n^2)}
15.33/9.34	
15.33/9.34	  12: evalaaron25->evalaaron2bb3in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  13: evalaaron25->evalaaron2bb4in, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  13: evalaaron25->evalaaron2bb4in, Arg_1: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  13: evalaaron25->evalaaron2bb4in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  13: evalaaron25->evalaaron2bb4in, Arg_3: max([Arg_0, Arg_4])+max([0, (1+2*Arg_2+-2*Arg_4)*max([1, 1+Arg_0])]) {O(n^2)}
15.33/9.34	
15.33/9.34	  13: evalaaron25->evalaaron2bb4in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  13: evalaaron25->evalaaron2bb4in, Arg_5: 0 {O(1)}
15.33/9.34	
15.33/9.34	  1: evalaaron2bb0in->evalaaron20, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  1: evalaaron2bb0in->evalaaron20, Arg_1: Arg_1 {O(n)}
15.33/9.34	
15.33/9.34	  1: evalaaron2bb0in->evalaaron20, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  1: evalaaron2bb0in->evalaaron20, Arg_3: Arg_3 {O(n)}
15.33/9.34	
15.33/9.34	  1: evalaaron2bb0in->evalaaron20, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  1: evalaaron2bb0in->evalaaron20, Arg_5: Arg_5 {O(n)}
15.33/9.34	
15.33/9.34	  7: evalaaron2bb1in->evalaaron2bb5in, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  7: evalaaron2bb1in->evalaaron2bb5in, Arg_1: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  7: evalaaron2bb1in->evalaaron2bb5in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  7: evalaaron2bb1in->evalaaron2bb5in, Arg_3: max([Arg_4, max([Arg_0, Arg_4])+max([0, (1+2*Arg_2+-2*Arg_4)*max([1, 1+Arg_0])])]) {O(n^2)}
15.33/9.34	
15.33/9.34	  7: evalaaron2bb1in->evalaaron2bb5in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  9: evalaaron2bb1in->evalaaron2bb2in, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  9: evalaaron2bb1in->evalaaron2bb2in, Arg_1: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  9: evalaaron2bb1in->evalaaron2bb2in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  9: evalaaron2bb1in->evalaaron2bb2in, Arg_3: max([Arg_0, Arg_4])+max([0, (1+2*Arg_2+-2*Arg_4)*max([1, 1+Arg_0])]) {O(n^2)}
15.33/9.34	
15.33/9.34	  9: evalaaron2bb1in->evalaaron2bb2in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  10: evalaaron2bb2in->evalaaron24, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  10: evalaaron2bb2in->evalaaron24, Arg_1: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  10: evalaaron2bb2in->evalaaron24, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  10: evalaaron2bb2in->evalaaron24, Arg_3: max([Arg_0, Arg_4])+max([0, (1+2*Arg_2+-2*Arg_4)*max([1, 1+Arg_0])]) {O(n^2)}
15.33/9.34	
15.33/9.34	  10: evalaaron2bb2in->evalaaron24, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  14: evalaaron2bb3in->evalaaron2bb1in, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  14: evalaaron2bb3in->evalaaron2bb1in, Arg_1: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  14: evalaaron2bb3in->evalaaron2bb1in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  14: evalaaron2bb3in->evalaaron2bb1in, Arg_3: max([Arg_0, Arg_4])+max([0, (1+2*Arg_2+-2*Arg_4)*max([1, 1+Arg_0])]) {O(n^2)}
15.33/9.34	
15.33/9.34	  14: evalaaron2bb3in->evalaaron2bb1in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  15: evalaaron2bb4in->evalaaron2bb1in, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  15: evalaaron2bb4in->evalaaron2bb1in, Arg_1: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  15: evalaaron2bb4in->evalaaron2bb1in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  15: evalaaron2bb4in->evalaaron2bb1in, Arg_3: max([Arg_0, Arg_4])+max([0, (1+2*Arg_2+-2*Arg_4)*max([1, 1+Arg_0])]) {O(n^2)}
15.33/9.34	
15.33/9.34	  15: evalaaron2bb4in->evalaaron2bb1in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  15: evalaaron2bb4in->evalaaron2bb1in, Arg_5: 0 {O(1)}
15.33/9.34	
15.33/9.34	  16: evalaaron2bb5in->evalaaron2stop, Arg_0: max([-1, Arg_0]) {O(n)}
15.33/9.34	
15.33/9.34	  16: evalaaron2bb5in->evalaaron2stop, Arg_1: max([Arg_2, Arg_1]) {O(n)}
15.33/9.34	
15.33/9.34	  16: evalaaron2bb5in->evalaaron2stop, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  16: evalaaron2bb5in->evalaaron2stop, Arg_3: max([Arg_4, max([Arg_3, max([Arg_0, Arg_4])+max([0, (1+2*Arg_2+-2*Arg_4)*max([1, 1+Arg_0])])])]) {O(n^2)}
15.33/9.34	
15.33/9.34	  16: evalaaron2bb5in->evalaaron2stop, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  0: evalaaron2start->evalaaron2bb0in, Arg_0: Arg_0 {O(n)}
15.33/9.34	
15.33/9.34	  0: evalaaron2start->evalaaron2bb0in, Arg_1: Arg_1 {O(n)}
15.33/9.34	
15.33/9.34	  0: evalaaron2start->evalaaron2bb0in, Arg_2: Arg_2 {O(n)}
15.33/9.34	
15.33/9.34	  0: evalaaron2start->evalaaron2bb0in, Arg_3: Arg_3 {O(n)}
15.33/9.34	
15.33/9.34	  0: evalaaron2start->evalaaron2bb0in, Arg_4: Arg_4 {O(n)}
15.33/9.34	
15.33/9.34	  0: evalaaron2start->evalaaron2bb0in, Arg_5: Arg_5 {O(n)}
15.33/9.34	
15.33/9.34	
15.33/9.34	----------------------------------------
15.33/9.34	
15.33/9.34	(2)
15.33/9.34	BOUNDS(1, nat(2 + 6 * Arg_2 + -6 * Arg_4) + nat(3 + 3 * Arg_2 + -3 * Arg_4) + max(6 + Arg_2 + -1 * Arg_4, 5) + max(4, 5 + 2 * Arg_2 + -2 * Arg_4))
15.33/9.34	
15.33/9.34	----------------------------------------
15.33/9.34	
15.33/9.34	(3) Loat Proof (FINISHED)
15.33/9.34	
15.33/9.34	
15.33/9.34	### Pre-processing the ITS problem ###
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	Initial linear ITS problem
15.33/9.34	
15.33/9.34	   Start location: evalaaron2start
15.33/9.34	
15.33/9.34	      0: evalaaron2start -> evalaaron2bb0in : [], cost: 1
15.33/9.34	
15.33/9.34	      1: evalaaron2bb0in -> evalaaron20 : [], cost: 1
15.33/9.34	
15.33/9.34	      2: evalaaron20 -> evalaaron21 : [], cost: 1
15.33/9.34	
15.33/9.34	      3: evalaaron21 -> evalaaron22 : [], cost: 1
15.33/9.34	
15.33/9.34	      4: evalaaron22 -> evalaaron23 : [], cost: 1
15.33/9.34	
15.33/9.34	      5: evalaaron23 -> evalaaron2bb1in : B'=C, D'=E, [ A>=0 ], cost: 1
15.33/9.34	
15.33/9.34	      6: evalaaron23 -> evalaaron2bb5in : [ 0>=1+A ], cost: 1
15.33/9.34	
15.33/9.34	      7: evalaaron2bb1in -> evalaaron2bb5in : [ D>=1+B ], cost: 1
15.33/9.34	
15.33/9.34	      8: evalaaron2bb1in -> evalaaron2bb5in : [ 0>=1+A ], cost: 1
15.33/9.34	
15.33/9.34	      9: evalaaron2bb1in -> evalaaron2bb2in : [ B>=D && A>=0 ], cost: 1
15.33/9.34	
15.33/9.34	     10: evalaaron2bb2in -> evalaaron24 : [], cost: 1
15.33/9.34	
15.33/9.34	     11: evalaaron24 -> evalaaron25 : F'=free, [], cost: 1
15.33/9.34	
15.33/9.34	     12: evalaaron25 -> evalaaron2bb3in : [ F>=1 ], cost: 1
15.33/9.34	
15.33/9.34	     13: evalaaron25 -> evalaaron2bb4in : [ 0>=F ], cost: 1
15.33/9.34	
15.33/9.34	     14: evalaaron2bb3in -> evalaaron2bb1in : B'=-1-A+B, [], cost: 1
15.33/9.34	
15.33/9.34	     15: evalaaron2bb4in -> evalaaron2bb1in : D'=1+D+A, [], cost: 1
15.33/9.34	
15.33/9.34	     16: evalaaron2bb5in -> evalaaron2stop : [], cost: 1
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	Removed unreachable and leaf rules:
15.33/9.34	
15.33/9.34	   Start location: evalaaron2start
15.33/9.34	
15.33/9.34	      0: evalaaron2start -> evalaaron2bb0in : [], cost: 1
15.33/9.34	
15.33/9.34	      1: evalaaron2bb0in -> evalaaron20 : [], cost: 1
15.33/9.34	
15.33/9.34	      2: evalaaron20 -> evalaaron21 : [], cost: 1
15.33/9.34	
15.33/9.34	      3: evalaaron21 -> evalaaron22 : [], cost: 1
15.33/9.34	
15.33/9.34	      4: evalaaron22 -> evalaaron23 : [], cost: 1
15.33/9.34	
15.33/9.34	      5: evalaaron23 -> evalaaron2bb1in : B'=C, D'=E, [ A>=0 ], cost: 1
15.33/9.34	
15.33/9.34	      9: evalaaron2bb1in -> evalaaron2bb2in : [ B>=D && A>=0 ], cost: 1
15.33/9.34	
15.33/9.34	     10: evalaaron2bb2in -> evalaaron24 : [], cost: 1
15.33/9.34	
15.33/9.34	     11: evalaaron24 -> evalaaron25 : F'=free, [], cost: 1
15.33/9.34	
15.33/9.34	     12: evalaaron25 -> evalaaron2bb3in : [ F>=1 ], cost: 1
15.33/9.34	
15.33/9.34	     13: evalaaron25 -> evalaaron2bb4in : [ 0>=F ], cost: 1
15.33/9.34	
15.33/9.34	     14: evalaaron2bb3in -> evalaaron2bb1in : B'=-1-A+B, [], cost: 1
15.33/9.34	
15.33/9.34	     15: evalaaron2bb4in -> evalaaron2bb1in : D'=1+D+A, [], cost: 1
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	### Simplification by acceleration and chaining ###
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	Eliminated locations (on linear paths):
15.33/9.34	
15.33/9.34	   Start location: evalaaron2start
15.33/9.34	
15.33/9.34	     21: evalaaron2start -> evalaaron2bb1in : B'=C, D'=E, [ A>=0 ], cost: 6
15.33/9.34	
15.33/9.34	     23: evalaaron2bb1in -> evalaaron25 : F'=free, [ B>=D && A>=0 ], cost: 3
15.33/9.34	
15.33/9.34	     24: evalaaron25 -> evalaaron2bb1in : B'=-1-A+B, [ F>=1 ], cost: 2
15.33/9.34	
15.33/9.34	     25: evalaaron25 -> evalaaron2bb1in : D'=1+D+A, [ 0>=F ], cost: 2
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	Eliminated locations (on tree-shaped paths):
15.33/9.34	
15.33/9.34	   Start location: evalaaron2start
15.33/9.34	
15.33/9.34	     21: evalaaron2start -> evalaaron2bb1in : B'=C, D'=E, [ A>=0 ], cost: 6
15.33/9.34	
15.33/9.34	     26: evalaaron2bb1in -> evalaaron2bb1in : B'=-1-A+B, F'=free, [ B>=D && A>=0 && free>=1 ], cost: 5
15.33/9.34	
15.33/9.34	     27: evalaaron2bb1in -> evalaaron2bb1in : D'=1+D+A, F'=free, [ B>=D && A>=0 && 0>=free ], cost: 5
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	Accelerating simple loops of location 6.
15.33/9.34	
15.33/9.34	   Accelerating the following rules:
15.33/9.34	
15.33/9.34	     26: evalaaron2bb1in -> evalaaron2bb1in : B'=-1-A+B, F'=free, [ B>=D && A>=0 && free>=1 ], cost: 5
15.33/9.34	
15.33/9.34	     27: evalaaron2bb1in -> evalaaron2bb1in : D'=1+D+A, F'=free, [ B>=D && A>=0 && 0>=free ], cost: 5
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	   Accelerated rule 26 with backward acceleration, yielding the new rule 28.
15.33/9.34	
15.33/9.34	   Accelerated rule 27 with backward acceleration, yielding the new rule 29.
15.33/9.34	
15.33/9.34	   Removing the simple loops: 26 27.
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	Accelerated all simple loops using metering functions (where possible):
15.33/9.34	
15.33/9.34	   Start location: evalaaron2start
15.33/9.34	
15.33/9.34	     21: evalaaron2start -> evalaaron2bb1in : B'=C, D'=E, [ A>=0 ], cost: 6
15.33/9.34	
15.33/9.34	     28: evalaaron2bb1in -> evalaaron2bb1in : B'=-A*k-k+B, F'=free, [ B>=D && A>=0 && free>=1 && k>0 && 1-k-A*(-1+k)+B>=D ], cost: 5*k
15.33/9.34	
15.33/9.34	     29: evalaaron2bb1in -> evalaaron2bb1in : D'=k_1*A+k_1+D, F'=free, [ B>=D && A>=0 && 0>=free && k_1>0 && B>=-1+k_1+D+(-1+k_1)*A ], cost: 5*k_1
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	Chained accelerated rules (with incoming rules):
15.33/9.34	
15.33/9.34	   Start location: evalaaron2start
15.33/9.34	
15.33/9.34	     21: evalaaron2start -> evalaaron2bb1in : B'=C, D'=E, [ A>=0 ], cost: 6
15.33/9.34	
15.33/9.34	     30: evalaaron2start -> evalaaron2bb1in : B'=C-A*k-k, D'=E, F'=free, [ A>=0 && C>=E && free>=1 && k>0 && 1+C-k-A*(-1+k)>=E ], cost: 6+5*k
15.33/9.34	
15.33/9.34	     31: evalaaron2start -> evalaaron2bb1in : B'=C, D'=k_1*A+k_1+E, F'=free, [ A>=0 && C>=E && 0>=free && k_1>0 && C>=-1+k_1+(-1+k_1)*A+E ], cost: 6+5*k_1
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	Removed unreachable locations (and leaf rules with constant cost):
15.33/9.34	
15.33/9.34	   Start location: evalaaron2start
15.33/9.34	
15.33/9.34	     30: evalaaron2start -> evalaaron2bb1in : B'=C-A*k-k, D'=E, F'=free, [ A>=0 && C>=E && free>=1 && k>0 && 1+C-k-A*(-1+k)>=E ], cost: 6+5*k
15.33/9.34	
15.33/9.34	     31: evalaaron2start -> evalaaron2bb1in : B'=C, D'=k_1*A+k_1+E, F'=free, [ A>=0 && C>=E && 0>=free && k_1>0 && C>=-1+k_1+(-1+k_1)*A+E ], cost: 6+5*k_1
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	### Computing asymptotic complexity ###
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	Fully simplified ITS problem
15.33/9.34	
15.33/9.34	   Start location: evalaaron2start
15.33/9.34	
15.33/9.34	     30: evalaaron2start -> evalaaron2bb1in : B'=C-A*k-k, D'=E, F'=free, [ A>=0 && C>=E && free>=1 && k>0 && 1+C-k-A*(-1+k)>=E ], cost: 6+5*k
15.33/9.34	
15.33/9.34	     31: evalaaron2start -> evalaaron2bb1in : B'=C, D'=k_1*A+k_1+E, F'=free, [ A>=0 && C>=E && 0>=free && k_1>0 && C>=-1+k_1+(-1+k_1)*A+E ], cost: 6+5*k_1
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	Computing asymptotic complexity for rule 30
15.33/9.34	
15.33/9.34	   Solved the limit problem by the following transformations:
15.33/9.34	
15.33/9.34	      Created initial limit problem:
15.33/9.34	
15.33/9.34	      6+5*k (+), 1+C-E (+/+!), 2+C-k-E-A*(-1+k) (+/+!), k (+/+!), free (+/+!), 1+A (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      removing all constraints (solved by SMT)
15.33/9.34	
15.33/9.34	      resulting limit problem: [solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (C) using substitution {C==n,A==0,k==1+n,free==n,E==0}
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      [solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	   Solved the limit problem by the following transformations:
15.33/9.34	
15.33/9.34	      Created initial limit problem:
15.33/9.34	
15.33/9.34	      6+5*k (+), 1+C-E (+/+!), 2+C-k-E-A*(-1+k) (+/+!), k (+/+!), free (+/+!), 1+A (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (C) using substitution {A==0}
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      1 (+/+!), 6+5*k (+), 1+C-E (+/+!), 2+C-k-E (+/+!), k (+/+!), free (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (C) using substitution {free==1}
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      1 (+/+!), 6+5*k (+), 1+C-E (+/+!), 2+C-k-E (+/+!), k (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (C) using substitution {E==1+C-k-A*(-1+k)}
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      1 (+/+!), 6+5*k (+), 1+A*(-1+k) (+/+!), k+A*(-1+k) (+/+!), k (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (B), deleting 1 (+/+!)
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      6+5*k (+), 1+A*(-1+k) (+/+!), k+A*(-1+k) (+/+!), k (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      removing all constraints (solved by SMT)
15.33/9.34	
15.33/9.34	      resulting limit problem: [solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (C) using substitution {A==1,k==n}
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      [solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	   Solved the limit problem by the following transformations:
15.33/9.34	
15.33/9.34	      Created initial limit problem:
15.33/9.34	
15.33/9.34	      6+5*k (+), 1+C-E (+/+!), 2+C-k-E-A*(-1+k) (+/+!), k (+/+!), free (+/+!), 1+A (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (C) using substitution {free==1}
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      1 (+/+!), 6+5*k (+), 1+C-E (+/+!), 2+C-k-E-A*(-1+k) (+/+!), k (+/+!), 1+A (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (C) using substitution {E==1+C-k-A*(-1+k)}
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      1 (+/+!), 6+5*k (+), k+A*(-1+k) (+/+!), k (+/+!), 1+A (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (B), deleting 1 (+/+!)
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      6+5*k (+), k+A*(-1+k) (+/+!), k (+/+!), 1+A (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      removing all constraints (solved by SMT)
15.33/9.34	
15.33/9.34	      resulting limit problem: [solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (C) using substitution {A==0,k==n}
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      [solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	   Solved the limit problem by the following transformations:
15.33/9.34	
15.33/9.34	      Created initial limit problem:
15.33/9.34	
15.33/9.34	      6+5*k (+), 1+C-E (+/+!), 2+C-k-E-A*(-1+k) (+/+!), k (+/+!), free (+/+!), 1+A (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (C) using substitution {A==0}
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      1 (+/+!), 6+5*k (+), 1+C-E (+/+!), 2+C-k-E (+/+!), k (+/+!), free (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (C) using substitution {E==1+C-k-A*(-1+k)}
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      1 (+/+!), 6+5*k (+), 1+A*(-1+k) (+/+!), k+A*(-1+k) (+/+!), k (+/+!), free (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (B), deleting 1 (+/+!)
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      6+5*k (+), 1+A*(-1+k) (+/+!), k+A*(-1+k) (+/+!), k (+/+!), free (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      removing all constraints (solved by SMT)
15.33/9.34	
15.33/9.34	      resulting limit problem: [solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (C) using substitution {A==0,k==1+n,free==n}
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      [solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	   Solved the limit problem by the following transformations:
15.33/9.34	
15.33/9.34	      Created initial limit problem:
15.33/9.34	
15.33/9.34	      6+5*k (+), 1+C-E (+/+!), 2+C-k-E-A*(-1+k) (+/+!), k (+/+!), free (+/+!), 1+A (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (C) using substitution {E==1+C-k-A*(-1+k)}
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      1 (+/+!), 6+5*k (+), k+A*(-1+k) (+/+!), k (+/+!), free (+/+!), 1+A (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (B), deleting 1 (+/+!)
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      6+5*k (+), k+A*(-1+k) (+/+!), k (+/+!), free (+/+!), 1+A (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      removing all constraints (solved by SMT)
15.33/9.34	
15.33/9.34	      resulting limit problem: [solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (C) using substitution {A==0,k==n,free==n}
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      [solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	   Solved the limit problem by the following transformations:
15.33/9.34	
15.33/9.34	      Created initial limit problem:
15.33/9.34	
15.33/9.34	      6+5*k (+), 1+C-E (+/+!), 2+C-k-E-A*(-1+k) (+/+!), k (+/+!), free (+/+!), 1+A (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (C) using substitution {A==0}
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      1 (+/+!), 6+5*k (+), 1+C-E (+/+!), 2+C-k-E (+/+!), k (+/+!), free (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (C) using substitution {free==1}
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      1 (+/+!), 6+5*k (+), 1+C-E (+/+!), 2+C-k-E (+/+!), k (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (B), deleting 1 (+/+!)
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.34	
15.33/9.34	      6+5*k (+), 1+C-E (+/+!), 2+C-k-E (+/+!), k (+/+!) [not solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      removing all constraints (solved by SMT)
15.33/9.34	
15.33/9.34	      resulting limit problem: [solved]
15.33/9.34	
15.33/9.34	
15.33/9.34	
15.33/9.34	      applying transformation rule (C) using substitution {C==0,k==n,E==-n}
15.33/9.34	
15.33/9.34	      resulting limit problem:
15.33/9.35	
15.33/9.35	      [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	   Solved the limit problem by the following transformations:
15.33/9.35	
15.33/9.35	      Created initial limit problem:
15.33/9.35	
15.33/9.35	      6+5*k (+), 1+C-E (+/+!), 2+C-k-E-A*(-1+k) (+/+!), k (+/+!), free (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {free==1}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      1 (+/+!), 6+5*k (+), 1+C-E (+/+!), 2+C-k-E-A*(-1+k) (+/+!), k (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (B), deleting 1 (+/+!)
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      6+5*k (+), 1+C-E (+/+!), 2+C-k-E-A*(-1+k) (+/+!), k (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      removing all constraints (solved by SMT)
15.33/9.35	
15.33/9.35	      resulting limit problem: [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {C==n,A==0,k==1+n,E==0}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	   Solved the limit problem by the following transformations:
15.33/9.35	
15.33/9.35	      Created initial limit problem:
15.33/9.35	
15.33/9.35	      6+5*k (+), 1+C-E (+/+!), 2+C-k-E-A*(-1+k) (+/+!), k (+/+!), free (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {A==0}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      1 (+/+!), 6+5*k (+), 1+C-E (+/+!), 2+C-k-E (+/+!), k (+/+!), free (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (B), deleting 1 (+/+!)
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      6+5*k (+), 1+C-E (+/+!), 2+C-k-E (+/+!), k (+/+!), free (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      removing all constraints (solved by SMT)
15.33/9.35	
15.33/9.35	      resulting limit problem: [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {C==0,k==n,free==n,E==-n}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	   Solution:
15.33/9.35	
15.33/9.35	      C / n
15.33/9.35	
15.33/9.35	      A / 0
15.33/9.35	
15.33/9.35	      k / 1+n
15.33/9.35	
15.33/9.35	      free / n
15.33/9.35	
15.33/9.35	      E / 0
15.33/9.35	
15.33/9.35	   Resulting cost 11+5*n has complexity: Poly(n^1)
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	Found new complexity Poly(n^1).
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	Computing asymptotic complexity for rule 31
15.33/9.35	
15.33/9.35	   Solved the limit problem by the following transformations:
15.33/9.35	
15.33/9.35	      Created initial limit problem:
15.33/9.35	
15.33/9.35	      1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-(-1+k_1)*A-E (+/+!), 1-free (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      removing all constraints (solved by SMT)
15.33/9.35	
15.33/9.35	      resulting limit problem: [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {C==n,k_1==n,A==0,free==-n,E==1}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	   Solved the limit problem by the following transformations:
15.33/9.35	
15.33/9.35	      Created initial limit problem:
15.33/9.35	
15.33/9.35	      1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-(-1+k_1)*A-E (+/+!), 1-free (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {A==0}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      1 (+/+!), 1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-E (+/+!), 1-free (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {free==0}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      1 (+/+!), 1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-E (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {C==-1+k_1+(-1+k_1)*A+E}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      1 (+/+!), 6+5*k_1 (+), k_1 (+/+!), k_1+(-1+k_1)*A (+/+!), 1+(-1+k_1)*A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (B), deleting 1 (+/+!)
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      6+5*k_1 (+), k_1 (+/+!), k_1+(-1+k_1)*A (+/+!), 1+(-1+k_1)*A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      removing all constraints (solved by SMT)
15.33/9.35	
15.33/9.35	      resulting limit problem: [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {k_1==n,A==1}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	   Solved the limit problem by the following transformations:
15.33/9.35	
15.33/9.35	      Created initial limit problem:
15.33/9.35	
15.33/9.35	      1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-(-1+k_1)*A-E (+/+!), 1-free (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {free==0}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      1 (+/+!), 1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-(-1+k_1)*A-E (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {C==-1+k_1+(-1+k_1)*A+E}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      1 (+/+!), 6+5*k_1 (+), k_1 (+/+!), k_1+(-1+k_1)*A (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (B), deleting 1 (+/+!)
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      6+5*k_1 (+), k_1 (+/+!), k_1+(-1+k_1)*A (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      removing all constraints (solved by SMT)
15.33/9.35	
15.33/9.35	      resulting limit problem: [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {k_1==n,A==0}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	   Solved the limit problem by the following transformations:
15.33/9.35	
15.33/9.35	      Created initial limit problem:
15.33/9.35	
15.33/9.35	      1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-(-1+k_1)*A-E (+/+!), 1-free (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {A==0}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      1 (+/+!), 1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-E (+/+!), 1-free (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {C==-1+k_1+(-1+k_1)*A+E}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      1 (+/+!), 6+5*k_1 (+), k_1 (+/+!), 1-free (+/+!), k_1+(-1+k_1)*A (+/+!), 1+(-1+k_1)*A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (B), deleting 1 (+/+!)
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      6+5*k_1 (+), k_1 (+/+!), 1-free (+/+!), k_1+(-1+k_1)*A (+/+!), 1+(-1+k_1)*A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      removing all constraints (solved by SMT)
15.33/9.35	
15.33/9.35	      resulting limit problem: [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {k_1==n,A==1,free==-n}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	   Solved the limit problem by the following transformations:
15.33/9.35	
15.33/9.35	      Created initial limit problem:
15.33/9.35	
15.33/9.35	      1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-(-1+k_1)*A-E (+/+!), 1-free (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {C==-1+k_1+(-1+k_1)*A+E}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      1 (+/+!), 6+5*k_1 (+), k_1 (+/+!), 1-free (+/+!), k_1+(-1+k_1)*A (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (B), deleting 1 (+/+!)
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      6+5*k_1 (+), k_1 (+/+!), 1-free (+/+!), k_1+(-1+k_1)*A (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      removing all constraints (solved by SMT)
15.33/9.35	
15.33/9.35	      resulting limit problem: [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {k_1==n,A==0,free==-n}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	   Solved the limit problem by the following transformations:
15.33/9.35	
15.33/9.35	      Created initial limit problem:
15.33/9.35	
15.33/9.35	      1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-(-1+k_1)*A-E (+/+!), 1-free (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {A==0}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      1 (+/+!), 1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-E (+/+!), 1-free (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {free==0}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      1 (+/+!), 1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-E (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (B), deleting 1 (+/+!)
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-E (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      removing all constraints (solved by SMT)
15.33/9.35	
15.33/9.35	      resulting limit problem: [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {C==0,k_1==n,E==-n}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	   Solved the limit problem by the following transformations:
15.33/9.35	
15.33/9.35	      Created initial limit problem:
15.33/9.35	
15.33/9.35	      1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-(-1+k_1)*A-E (+/+!), 1-free (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {free==0}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      1 (+/+!), 1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-(-1+k_1)*A-E (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (B), deleting 1 (+/+!)
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-(-1+k_1)*A-E (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      removing all constraints (solved by SMT)
15.33/9.35	
15.33/9.35	      resulting limit problem: [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {C==n,k_1==-1+n,A==0,E==2}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	   Solved the limit problem by the following transformations:
15.33/9.35	
15.33/9.35	      Created initial limit problem:
15.33/9.35	
15.33/9.35	      1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-(-1+k_1)*A-E (+/+!), 1-free (+/+!), 1+A (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {A==0}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      1 (+/+!), 1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-E (+/+!), 1-free (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (B), deleting 1 (+/+!)
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      1+C-E (+/+!), 6+5*k_1 (+), k_1 (+/+!), 2+C-k_1-E (+/+!), 1-free (+/+!) [not solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      removing all constraints (solved by SMT)
15.33/9.35	
15.33/9.35	      resulting limit problem: [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	      applying transformation rule (C) using substitution {C==0,k_1==n,free==-n,E==-n}
15.33/9.35	
15.33/9.35	      resulting limit problem:
15.33/9.35	
15.33/9.35	      [solved]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	   Solution:
15.33/9.35	
15.33/9.35	      C / n
15.33/9.35	
15.33/9.35	      k_1 / n
15.33/9.35	
15.33/9.35	      A / 0
15.33/9.35	
15.33/9.35	      free / -n
15.33/9.35	
15.33/9.35	      E / 1
15.33/9.35	
15.33/9.35	   Resulting cost 6+5*n has complexity: Poly(n^1)
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	Obtained the following overall complexity (w.r.t. the length of the input n):
15.33/9.35	
15.33/9.35	   Complexity:  Poly(n^1)
15.33/9.35	
15.33/9.35	   Cpx degree:  1
15.33/9.35	
15.33/9.35	   Solved cost: 11+5*n
15.33/9.35	
15.33/9.35	   Rule cost:   6+5*k
15.33/9.35	
15.33/9.35	   Rule guard:  [ A>=0 && C>=E && free>=1 && k>0 && 1+C-k-A*(-1+k)>=E ]
15.33/9.35	
15.33/9.35	
15.33/9.35	
15.33/9.35	WORST_CASE(Omega(n^1),?)
15.33/9.35	
15.33/9.35	
15.33/9.35	----------------------------------------
15.33/9.35	
15.33/9.35	(4)
15.33/9.35	BOUNDS(n^1, INF)
15.41/9.38	EOF