17.74/12.48	WORST_CASE(Omega(n^1), O(n^2))
17.74/12.49	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
17.74/12.49	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
17.74/12.49	
17.74/12.49	
17.74/12.49	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(13, 7 + 3 * Arg_0) + max(3 * Arg_0, 6) * nat(Arg_0) + nat(Arg_0 * max(3 * Arg_0, 6)) * nat(Arg_0) + nat(Arg_0 * max(3 * Arg_0, 6)) + nat(8 * Arg_0) + max(3 + Arg_0, 3) + max(4 * Arg_0, 8)).
17.74/12.49	
17.74/12.49	(0) CpxIntTrs
17.74/12.49	(1) Loat Proof [FINISHED, 1819 ms]
17.74/12.49	(2) BOUNDS(n^1, INF)
17.74/12.49	
17.74/12.49	
17.74/12.49	----------------------------------------
17.74/12.49	
17.74/12.49	(0)
17.74/12.49	Obligation:
17.74/12.49	Complexity Int TRS consisting of the following rules:
17.74/12.49	eval_perfect_start(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb0_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: TRUE
17.74/12.49	eval_perfect_bb0_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_0(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: TRUE
17.74/12.49	eval_perfect_0(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_1(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: TRUE
17.74/12.49	eval_perfect_1(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb6_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_x <= 1
17.74/12.49	eval_perfect_1(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb1_in(v__y3_0, v_1, v_6, v_x, v_x, v_y2_1, v_x)) :|: v_x > 1
17.74/12.49	eval_perfect_bb1_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb2_in(v__y3_0, v_y1_0_sink - 1, v_6, v_x, v_y1_0_sink, v_x, v_y3_0)) :|: v_y1_0_sink - 1 > 0
17.74/12.49	eval_perfect_bb1_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb5_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y1_0_sink - 1 <= 0
17.74/12.49	eval_perfect_bb2_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb3_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y2_1 >= v_1
17.74/12.49	eval_perfect_bb2_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb4_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y2_1 < v_1
17.74/12.49	eval_perfect_bb3_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb2_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1 - v_1, v_y3_0)) :|: TRUE
17.74/12.49	eval_perfect_bb4_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_7(v__y3_0, v_1, v_y3_0 - v_1, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: TRUE
17.74/12.49	eval_perfect_7(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_8(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: TRUE
17.74/12.49	eval_perfect_8(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_9(v_6, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y2_1 >= 0 && v_y2_1 <= 0
17.74/12.49	eval_perfect_8(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_9(v_y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y2_1 < 0
17.74/12.49	eval_perfect_8(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_9(v_y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y2_1 > 0
17.74/12.49	eval_perfect_9(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_10(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: TRUE
17.74/12.49	eval_perfect_10(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_11(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: TRUE
17.74/12.49	eval_perfect_11(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb1_in(v__y3_0, v_1, v_6, v_x, v_1, v_y2_1, v__y3_0)) :|: TRUE
17.74/12.49	eval_perfect_bb5_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb6_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y3_0 < 0
17.74/12.49	eval_perfect_bb5_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb6_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y3_0 > 0
17.74/12.49	eval_perfect_bb5_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb6_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y3_0 >= 0 && v_y3_0 <= 0
17.74/12.49	eval_perfect_bb6_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_stop(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: TRUE
17.74/12.49	
17.74/12.49	The start-symbols are:[eval_perfect_start_7]
17.74/12.49	
17.74/12.49	
17.74/12.49	----------------------------------------
17.74/12.49	
17.74/12.49	(1) Loat Proof (FINISHED)
17.74/12.49	
17.74/12.49	
17.74/12.49	### Pre-processing the ITS problem ###
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	Initial linear ITS problem
17.74/12.49	
17.74/12.49	   Start location: evalperfectstart
17.74/12.49	
17.74/12.49	      0: evalperfectstart -> evalperfectbb0in : [], cost: 1
17.74/12.49	
17.74/12.49	      1: evalperfectbb0in -> evalperfect0 : [], cost: 1
17.74/12.49	
17.74/12.49	      2: evalperfect0 -> evalperfect1 : [], cost: 1
17.74/12.49	
17.74/12.49	      3: evalperfect1 -> evalperfectbb6in : [ 1>=A ], cost: 1
17.74/12.49	
17.74/12.49	      4: evalperfect1 -> evalperfectbb1in : B'=A, C'=A, [ A>=2 ], cost: 1
17.74/12.49	
17.74/12.49	      5: evalperfectbb1in -> evalperfectbb2in : D'=-1+B, E'=A, [ B>=2 ], cost: 1
17.74/12.49	
17.74/12.49	      6: evalperfectbb1in -> evalperfectbb5in : [ 1>=B ], cost: 1
17.74/12.49	
17.74/12.49	      7: evalperfectbb2in -> evalperfectbb3in : [ E>=D ], cost: 1
17.74/12.49	
17.74/12.49	      8: evalperfectbb2in -> evalperfectbb4in : [ D>=1+E ], cost: 1
17.74/12.49	
17.74/12.49	      9: evalperfectbb3in -> evalperfectbb2in : E'=-D+E, [], cost: 1
17.74/12.49	
17.74/12.49	     10: evalperfectbb4in -> evalperfect7 : F'=C-D, [], cost: 1
17.74/12.49	
17.74/12.49	     11: evalperfect7 -> evalperfect8 : [], cost: 1
17.74/12.49	
17.74/12.49	     12: evalperfect8 -> evalperfect9 : G'=F, [ E==0 ], cost: 1
17.74/12.49	
17.74/12.49	     13: evalperfect8 -> evalperfect9 : G'=C, [ 0>=1+E ], cost: 1
17.74/12.49	
17.74/12.49	     14: evalperfect8 -> evalperfect9 : G'=C, [ E>=1 ], cost: 1
17.74/12.49	
17.74/12.49	     15: evalperfect9 -> evalperfect10 : [], cost: 1
17.74/12.49	
17.74/12.49	     16: evalperfect10 -> evalperfect11 : [], cost: 1
17.74/12.49	
17.74/12.49	     17: evalperfect11 -> evalperfectbb1in : B'=D, C'=G, [], cost: 1
17.74/12.49	
17.74/12.49	     18: evalperfectbb5in -> evalperfectbb6in : [ 0>=1+C ], cost: 1
17.74/12.49	
17.74/12.49	     19: evalperfectbb5in -> evalperfectbb6in : [ C>=1 ], cost: 1
17.74/12.49	
17.74/12.49	     20: evalperfectbb5in -> evalperfectbb6in : [ C==0 ], cost: 1
17.74/12.49	
17.74/12.49	     21: evalperfectbb6in -> evalperfectstop : [], cost: 1
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	Removed unreachable and leaf rules:
17.74/12.49	
17.74/12.49	   Start location: evalperfectstart
17.74/12.49	
17.74/12.49	      0: evalperfectstart -> evalperfectbb0in : [], cost: 1
17.74/12.49	
17.74/12.49	      1: evalperfectbb0in -> evalperfect0 : [], cost: 1
17.74/12.49	
17.74/12.49	      2: evalperfect0 -> evalperfect1 : [], cost: 1
17.74/12.49	
17.74/12.49	      4: evalperfect1 -> evalperfectbb1in : B'=A, C'=A, [ A>=2 ], cost: 1
17.74/12.49	
17.74/12.49	      5: evalperfectbb1in -> evalperfectbb2in : D'=-1+B, E'=A, [ B>=2 ], cost: 1
17.74/12.49	
17.74/12.49	      7: evalperfectbb2in -> evalperfectbb3in : [ E>=D ], cost: 1
17.74/12.49	
17.74/12.49	      8: evalperfectbb2in -> evalperfectbb4in : [ D>=1+E ], cost: 1
17.74/12.49	
17.74/12.49	      9: evalperfectbb3in -> evalperfectbb2in : E'=-D+E, [], cost: 1
17.74/12.49	
17.74/12.49	     10: evalperfectbb4in -> evalperfect7 : F'=C-D, [], cost: 1
17.74/12.49	
17.74/12.49	     11: evalperfect7 -> evalperfect8 : [], cost: 1
17.74/12.49	
17.74/12.49	     12: evalperfect8 -> evalperfect9 : G'=F, [ E==0 ], cost: 1
17.74/12.49	
17.74/12.49	     13: evalperfect8 -> evalperfect9 : G'=C, [ 0>=1+E ], cost: 1
17.74/12.49	
17.74/12.49	     14: evalperfect8 -> evalperfect9 : G'=C, [ E>=1 ], cost: 1
17.74/12.49	
17.74/12.49	     15: evalperfect9 -> evalperfect10 : [], cost: 1
17.74/12.49	
17.74/12.49	     16: evalperfect10 -> evalperfect11 : [], cost: 1
17.74/12.49	
17.74/12.49	     17: evalperfect11 -> evalperfectbb1in : B'=D, C'=G, [], cost: 1
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	### Simplification by acceleration and chaining ###
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	Eliminated locations (on linear paths):
17.74/12.49	
17.74/12.49	   Start location: evalperfectstart
17.74/12.49	
17.74/12.49	     24: evalperfectstart -> evalperfectbb1in : B'=A, C'=A, [ A>=2 ], cost: 4
17.74/12.49	
17.74/12.49	      5: evalperfectbb1in -> evalperfectbb2in : D'=-1+B, E'=A, [ B>=2 ], cost: 1
17.74/12.49	
17.74/12.49	     25: evalperfectbb2in -> evalperfectbb2in : E'=-D+E, [ E>=D ], cost: 2
17.74/12.49	
17.74/12.49	     27: evalperfectbb2in -> evalperfect8 : F'=C-D, [ D>=1+E ], cost: 3
17.74/12.49	
17.74/12.49	     12: evalperfect8 -> evalperfect9 : G'=F, [ E==0 ], cost: 1
17.74/12.49	
17.74/12.49	     13: evalperfect8 -> evalperfect9 : G'=C, [ 0>=1+E ], cost: 1
17.74/12.49	
17.74/12.49	     14: evalperfect8 -> evalperfect9 : G'=C, [ E>=1 ], cost: 1
17.74/12.49	
17.74/12.49	     29: evalperfect9 -> evalperfectbb1in : B'=D, C'=G, [], cost: 3
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	Accelerating simple loops of location 5.
17.74/12.49	
17.74/12.49	   Accelerating the following rules:
17.74/12.49	
17.74/12.49	     25: evalperfectbb2in -> evalperfectbb2in : E'=-D+E, [ E>=D ], cost: 2
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	   Found no metering function for rule 25.
17.74/12.49	
17.74/12.49	   Removing the simple loops:.
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	Accelerated all simple loops using metering functions (where possible):
17.74/12.49	
17.74/12.49	   Start location: evalperfectstart
17.74/12.49	
17.74/12.49	     24: evalperfectstart -> evalperfectbb1in : B'=A, C'=A, [ A>=2 ], cost: 4
17.74/12.49	
17.74/12.49	      5: evalperfectbb1in -> evalperfectbb2in : D'=-1+B, E'=A, [ B>=2 ], cost: 1
17.74/12.49	
17.74/12.49	     25: evalperfectbb2in -> evalperfectbb2in : E'=-D+E, [ E>=D ], cost: 2
17.74/12.49	
17.74/12.49	     27: evalperfectbb2in -> evalperfect8 : F'=C-D, [ D>=1+E ], cost: 3
17.74/12.49	
17.74/12.49	     12: evalperfect8 -> evalperfect9 : G'=F, [ E==0 ], cost: 1
17.74/12.49	
17.74/12.49	     13: evalperfect8 -> evalperfect9 : G'=C, [ 0>=1+E ], cost: 1
17.74/12.49	
17.74/12.49	     14: evalperfect8 -> evalperfect9 : G'=C, [ E>=1 ], cost: 1
17.74/12.49	
17.74/12.49	     29: evalperfect9 -> evalperfectbb1in : B'=D, C'=G, [], cost: 3
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	Chained accelerated rules (with incoming rules):
17.74/12.49	
17.74/12.49	   Start location: evalperfectstart
17.74/12.49	
17.74/12.49	     24: evalperfectstart -> evalperfectbb1in : B'=A, C'=A, [ A>=2 ], cost: 4
17.74/12.49	
17.74/12.49	      5: evalperfectbb1in -> evalperfectbb2in : D'=-1+B, E'=A, [ B>=2 ], cost: 1
17.74/12.49	
17.74/12.49	     30: evalperfectbb1in -> evalperfectbb2in : D'=-1+B, E'=1+A-B, [ B>=2 && A>=-1+B ], cost: 3
17.74/12.49	
17.74/12.49	     27: evalperfectbb2in -> evalperfect8 : F'=C-D, [ D>=1+E ], cost: 3
17.74/12.49	
17.74/12.49	     12: evalperfect8 -> evalperfect9 : G'=F, [ E==0 ], cost: 1
17.74/12.49	
17.74/12.49	     13: evalperfect8 -> evalperfect9 : G'=C, [ 0>=1+E ], cost: 1
17.74/12.49	
17.74/12.49	     14: evalperfect8 -> evalperfect9 : G'=C, [ E>=1 ], cost: 1
17.74/12.49	
17.74/12.49	     29: evalperfect9 -> evalperfectbb1in : B'=D, C'=G, [], cost: 3
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	Eliminated locations (on tree-shaped paths):
17.74/12.49	
17.74/12.49	   Start location: evalperfectstart
17.74/12.49	
17.74/12.49	     24: evalperfectstart -> evalperfectbb1in : B'=A, C'=A, [ A>=2 ], cost: 4
17.74/12.49	
17.74/12.49	     31: evalperfectbb1in -> evalperfect8 : D'=-1+B, E'=A, F'=1+C-B, [ B>=2 && -1+B>=1+A ], cost: 4
17.74/12.49	
17.74/12.49	     32: evalperfectbb1in -> evalperfect8 : D'=-1+B, E'=1+A-B, F'=1+C-B, [ B>=2 && A>=-1+B && -1+B>=2+A-B ], cost: 6
17.74/12.49	
17.74/12.49	     33: evalperfect8 -> evalperfectbb1in : B'=D, C'=F, G'=F, [ E==0 ], cost: 4
17.74/12.49	
17.74/12.49	     34: evalperfect8 -> evalperfectbb1in : B'=D, C'=C, G'=C, [ 0>=1+E ], cost: 4
17.74/12.49	
17.74/12.49	     35: evalperfect8 -> evalperfectbb1in : B'=D, C'=C, G'=C, [ E>=1 ], cost: 4
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	Eliminated locations (on tree-shaped paths):
17.74/12.49	
17.74/12.49	   Start location: evalperfectstart
17.74/12.49	
17.74/12.49	     24: evalperfectstart -> evalperfectbb1in : B'=A, C'=A, [ A>=2 ], cost: 4
17.74/12.49	
17.74/12.49	     36: evalperfectbb1in -> evalperfectbb1in : B'=-1+B, C'=1+C-B, D'=-1+B, E'=A, F'=1+C-B, G'=1+C-B, [ B>=2 && -1+B>=1+A && A==0 ], cost: 8
17.74/12.49	
17.74/12.49	     37: evalperfectbb1in -> evalperfectbb1in : B'=-1+B, C'=C, D'=-1+B, E'=A, F'=1+C-B, G'=C, [ B>=2 && -1+B>=1+A && 0>=1+A ], cost: 8
17.74/12.49	
17.74/12.49	     38: evalperfectbb1in -> evalperfectbb1in : B'=-1+B, C'=C, D'=-1+B, E'=A, F'=1+C-B, G'=C, [ B>=2 && -1+B>=1+A && A>=1 ], cost: 8
17.74/12.49	
17.74/12.49	     39: evalperfectbb1in -> evalperfectbb1in : B'=-1+B, C'=1+C-B, D'=-1+B, E'=1+A-B, F'=1+C-B, G'=1+C-B, [ B>=2 && -1+B>=2+A-B && 1+A-B==0 ], cost: 10
17.74/12.49	
17.74/12.49	     40: evalperfectbb1in -> evalperfectbb1in : B'=-1+B, C'=C, D'=-1+B, E'=1+A-B, F'=1+C-B, G'=C, [ B>=2 && -1+B>=2+A-B && 1+A-B>=1 ], cost: 10
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	Accelerating simple loops of location 4.
17.74/12.49	
17.74/12.49	   Simplified some of the simple loops (and removed duplicate rules).
17.74/12.49	
17.74/12.49	   Accelerating the following rules:
17.74/12.49	
17.74/12.49	     36: evalperfectbb1in -> evalperfectbb1in : B'=-1+B, C'=1+C-B, D'=-1+B, E'=A, F'=1+C-B, G'=1+C-B, [ B>=2 && -1+B>=1+A && A==0 ], cost: 8
17.74/12.49	
17.74/12.49	     37: evalperfectbb1in -> evalperfectbb1in : B'=-1+B, D'=-1+B, E'=A, F'=1+C-B, G'=C, [ B>=2 && -1+B>=1+A && 0>=1+A ], cost: 8
17.74/12.49	
17.74/12.49	     38: evalperfectbb1in -> evalperfectbb1in : B'=-1+B, D'=-1+B, E'=A, F'=1+C-B, G'=C, [ B>=2 && -1+B>=1+A && A>=1 ], cost: 8
17.74/12.49	
17.74/12.49	     39: evalperfectbb1in -> evalperfectbb1in : B'=-1+B, C'=1+C-B, D'=-1+B, E'=1+A-B, F'=1+C-B, G'=1+C-B, [ B>=2 && -1+B>=2+A-B && 1+A-B==0 ], cost: 10
17.74/12.49	
17.74/12.49	     40: evalperfectbb1in -> evalperfectbb1in : B'=-1+B, D'=-1+B, E'=1+A-B, F'=1+C-B, G'=C, [ B>=2 && -1+B>=2+A-B && 1+A-B>=1 ], cost: 10
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	   Accelerated rule 36 with metering function -1-A+B, yielding the new rule 41.
17.74/12.49	
17.74/12.49	   Accelerated rule 37 with metering function -1+B, yielding the new rule 42.
17.74/12.49	
17.74/12.49	   Accelerated rule 38 with metering function -1-A+B, yielding the new rule 43.
17.74/12.49	
17.74/12.49	   Accelerated rule 39 with metering function -1-A+B, yielding the new rule 44.
17.74/12.49	
17.74/12.49	   Accelerated rule 40 with metering function meter (where 2*meter==-2-A+2*B), yielding the new rule 45.
17.74/12.49	
17.74/12.49	      During metering: Instantiating temporary variables by {meter==1}
17.74/12.49	
17.74/12.49	   Removing the simple loops: 36 37 38 39 40.
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	Accelerated all simple loops using metering functions (where possible):
17.74/12.49	
17.74/12.49	   Start location: evalperfectstart
17.74/12.49	
17.74/12.49	     24: evalperfectstart -> evalperfectbb1in : B'=A, C'=A, [ A>=2 ], cost: 4
17.74/12.49	
17.74/12.49	     41: evalperfectbb1in -> evalperfectbb1in : B'=1+A, C'=-5/2+C+1/2*(1+A-B)^2-3/2*A+(1+A-B)*B+3/2*B, D'=1+A, E'=A, F'=-7/2+C+1/2*(1+A-B)^2-3/2*A+(1+A-B)*B+3/2*B, G'=-7/2+C+1/2*(1+A-B)^2-3/2*A+(1+A-B)*B+3/2*B, [ B>=2 && -1+B>=1+A && A==0 ], cost: -8-8*A+8*B
17.74/12.49	
17.74/12.49	     42: evalperfectbb1in -> evalperfectbb1in : B'=1, D'=1, E'=A, F'=-1+C, G'=C, [ B>=2 && -1+B>=1+A && 0>=1+A ], cost: -8+8*B
17.74/12.49	
17.74/12.49	     43: evalperfectbb1in -> evalperfectbb1in : B'=1+A, D'=1+A, E'=A, F'=-1+C-A, G'=C, [ B>=2 && -1+B>=1+A && A>=1 ], cost: -8-8*A+8*B
17.74/12.49	
17.74/12.49	     44: evalperfectbb1in -> evalperfectbb1in : B'=1+A, C'=-5/2+C+1/2*(1+A-B)^2-3/2*A+(1+A-B)*B+3/2*B, D'=1+A, E'=-1, F'=-7/2+C+1/2*(1+A-B)^2-3/2*A+(1+A-B)*B+3/2*B, G'=-7/2+C+1/2*(1+A-B)^2-3/2*A+(1+A-B)*B+3/2*B, [ B>=2 && -1+B>=2+A-B && 1+A-B==0 && -1-A+B>=1 ], cost: -10-10*A+10*B
17.74/12.49	
17.74/12.49	     45: evalperfectbb1in -> evalperfectbb1in : B'=-meter+B, D'=-meter+B, E'=meter+A-B, F'=meter+C-B, G'=C, [ B>=2 && -1+B>=2+A-B && 1+A-B>=1 && 2*meter==-2-A+2*B && meter>=1 ], cost: 10*meter
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	Chained accelerated rules (with incoming rules):
17.74/12.49	
17.74/12.49	   Start location: evalperfectstart
17.74/12.49	
17.74/12.49	     24: evalperfectstart -> evalperfectbb1in : B'=A, C'=A, [ A>=2 ], cost: 4
17.74/12.49	
17.74/12.49	     46: evalperfectstart -> evalperfectbb1in : B'=-meter+A, C'=A, D'=-meter+A, E'=meter, F'=meter, G'=A, [ -1+A>=2 && 2*meter==-2+A && meter>=1 ], cost: 4+10*meter
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	Removed unreachable locations (and leaf rules with constant cost):
17.74/12.49	
17.74/12.49	   Start location: evalperfectstart
17.74/12.49	
17.74/12.49	     46: evalperfectstart -> evalperfectbb1in : B'=-meter+A, C'=A, D'=-meter+A, E'=meter, F'=meter, G'=A, [ -1+A>=2 && 2*meter==-2+A && meter>=1 ], cost: 4+10*meter
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	### Computing asymptotic complexity ###
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	Fully simplified ITS problem
17.74/12.49	
17.74/12.49	   Start location: evalperfectstart
17.74/12.49	
17.74/12.49	     46: evalperfectstart -> evalperfectbb1in : B'=-meter+A, C'=A, D'=-meter+A, E'=meter, F'=meter, G'=A, [ -1+A>=2 && 2*meter==-2+A && meter>=1 ], cost: 4+10*meter
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	Computing asymptotic complexity for rule 46
17.74/12.49	
17.74/12.49	   Solved the limit problem by the following transformations:
17.74/12.49	
17.74/12.49	      Created initial limit problem:
17.74/12.49	
17.74/12.49	      3+2*meter-A (+/+!), -1-2*meter+A (+/+!), -2+A (+/+!), 4+10*meter (+) [not solved]
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	      applying transformation rule (C) using substitution {A==2+2*meter}
17.74/12.49	
17.74/12.49	      resulting limit problem:
17.74/12.49	
17.74/12.49	      1 (+/+!), 2*meter (+/+!), 4+10*meter (+) [not solved]
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	      applying transformation rule (B), deleting 1 (+/+!)
17.74/12.49	
17.74/12.49	      resulting limit problem:
17.74/12.49	
17.74/12.49	      2*meter (+/+!), 4+10*meter (+) [not solved]
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	      removing all constraints (solved by SMT)
17.74/12.49	
17.74/12.49	      resulting limit problem: [solved]
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	      applying transformation rule (C) using substitution {meter==n}
17.74/12.49	
17.74/12.49	      resulting limit problem:
17.74/12.49	
17.74/12.49	      [solved]
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	   Solved the limit problem by the following transformations:
17.74/12.49	
17.74/12.49	      Created initial limit problem:
17.74/12.49	
17.74/12.49	      3+2*meter-A (+/+!), -1-2*meter+A (+/+!), -2+A (+/+!), 4+10*meter (+) [not solved]
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	      applying transformation rule (C) using substitution {A==2+2*meter}
17.74/12.49	
17.74/12.49	      resulting limit problem:
17.74/12.49	
17.74/12.49	      1 (+/+!), 2*meter (+/+!), 4+10*meter (+) [not solved]
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	      applying transformation rule (B), deleting 1 (+/+!)
17.74/12.49	
17.74/12.49	      resulting limit problem:
17.74/12.49	
17.74/12.49	      2*meter (+/+!), 4+10*meter (+) [not solved]
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	      removing all constraints (solved by SMT)
17.74/12.49	
17.74/12.49	      resulting limit problem: [solved]
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	      applying transformation rule (C) using substitution {meter==n}
17.74/12.49	
17.74/12.49	      resulting limit problem:
17.74/12.49	
17.74/12.49	      [solved]
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	   Solution:
17.74/12.49	
17.74/12.49	      meter / n
17.74/12.49	
17.74/12.49	      A / 2+2*n
17.74/12.49	
17.74/12.49	   Resulting cost 4+10*n has complexity: Poly(n^1)
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	Found new complexity Poly(n^1).
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	Obtained the following overall complexity (w.r.t. the length of the input n):
17.74/12.49	
17.74/12.49	   Complexity:  Poly(n^1)
17.74/12.49	
17.74/12.49	   Cpx degree:  1
17.74/12.49	
17.74/12.49	   Solved cost: 4+10*n
17.74/12.49	
17.74/12.49	   Rule cost:   4+10*meter
17.74/12.49	
17.74/12.49	   Rule guard:  [ -1+A>=2 && 2*meter==-2+A ]
17.74/12.49	
17.74/12.49	
17.74/12.49	
17.74/12.49	WORST_CASE(Omega(n^1),?)
17.74/12.49	
17.74/12.49	
17.74/12.49	----------------------------------------
17.74/12.49	
17.74/12.49	(2)
17.74/12.49	BOUNDS(n^1, INF)
17.74/12.52	EOF