16.20/11.11	WORST_CASE(Omega(n^1), O(n^2))
16.20/11.13	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
16.20/11.13	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
16.20/11.13	
16.20/11.13	
16.20/11.13	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(7 + Arg_0 * max(18, 9 * Arg_0), 7) + nat(Arg_0 * max(18, 9 * Arg_0)) * nat(Arg_0) + max(3, 3 * Arg_0) * nat(Arg_0) + max(6 * Arg_0, 6) + nat(7 * Arg_0) + max(3, 3 + Arg_0)).
16.20/11.13	
16.20/11.13	(0) CpxIntTrs
16.20/11.13	(1) Loat Proof [FINISHED, 1817 ms]
16.20/11.13	(2) BOUNDS(n^1, INF)
16.20/11.13	
16.20/11.13	
16.20/11.13	----------------------------------------
16.20/11.13	
16.20/11.13	(0)
16.20/11.13	Obligation:
16.20/11.13	Complexity Int TRS consisting of the following rules:
16.20/11.13	eval_perfect2_start(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb0_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE
16.20/11.13	eval_perfect2_bb0_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_0(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE
16.20/11.13	eval_perfect2_0(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_1(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE
16.20/11.13	eval_perfect2_1(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb3_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_x <= 0
16.20/11.13	eval_perfect2_1(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb1_in(v__y3_0, v_1, v_8, v_x, v_x, v_y2_1, v_x)) :|: v_x > 0
16.20/11.13	eval_perfect2_bb1_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb2_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y1_0 - 1 >= 0 && v_y1_0 - 1 <= 0
16.20/11.13	eval_perfect2_bb1_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb4_in(v__y3_0, v_y1_0 - 1, v_8, v_x, v_y1_0, v_x, v_y3_0)) :|: v_y1_0 - 1 < 0
16.20/11.13	eval_perfect2_bb1_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb4_in(v__y3_0, v_y1_0 - 1, v_8, v_x, v_y1_0, v_x, v_y3_0)) :|: v_y1_0 - 1 > 0
16.20/11.13	eval_perfect2_bb2_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb3_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y3_0 < 0
16.20/11.13	eval_perfect2_bb2_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb3_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y3_0 > 0
16.20/11.13	eval_perfect2_bb2_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb3_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y3_0 >= 0 && v_y3_0 <= 0
16.20/11.13	eval_perfect2_bb3_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_stop(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE
16.20/11.13	eval_perfect2_bb4_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb5_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y2_1 >= v_1
16.20/11.13	eval_perfect2_bb4_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb6_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y2_1 < v_1
16.20/11.13	eval_perfect2_bb5_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb4_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1 - v_1, v_y3_0)) :|: TRUE
16.20/11.13	eval_perfect2_bb6_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_9(v__y3_0, v_1, v_y3_0 - v_1, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE
16.20/11.13	eval_perfect2_9(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_10(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE
16.20/11.13	eval_perfect2_10(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_11(v_8, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y2_1 >= 0 && v_y2_1 <= 0
16.20/11.13	eval_perfect2_10(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_11(v_y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y2_1 < 0
16.20/11.13	eval_perfect2_10(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_11(v_y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y2_1 > 0
16.20/11.13	eval_perfect2_11(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_12(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE
16.20/11.13	eval_perfect2_12(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb1_in(v__y3_0, v_1, v_8, v_x, v_1, v_y2_1, v__y3_0)) :|: TRUE
16.20/11.13	
16.20/11.13	The start-symbols are:[eval_perfect2_start_7]
16.20/11.13	
16.20/11.13	
16.20/11.13	----------------------------------------
16.20/11.13	
16.20/11.13	(1) Loat Proof (FINISHED)
16.20/11.13	
16.20/11.13	
16.20/11.13	### Pre-processing the ITS problem ###
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	Initial linear ITS problem
16.20/11.13	
16.20/11.13	   Start location: evalperfect2start
16.20/11.13	
16.20/11.13	      0: evalperfect2start -> evalperfect2bb0in : [], cost: 1
16.20/11.13	
16.20/11.13	      1: evalperfect2bb0in -> evalperfect20 : [], cost: 1
16.20/11.13	
16.20/11.13	      2: evalperfect20 -> evalperfect21 : [], cost: 1
16.20/11.13	
16.20/11.13	      3: evalperfect21 -> evalperfect2bb3in : [ 0>=A ], cost: 1
16.20/11.13	
16.20/11.13	      4: evalperfect21 -> evalperfect2bb1in : B'=A, C'=A, [ A>=1 ], cost: 1
16.20/11.13	
16.20/11.13	      5: evalperfect2bb1in -> evalperfect2bb2in : [ B==1 ], cost: 1
16.20/11.13	
16.20/11.13	      6: evalperfect2bb1in -> evalperfect2bb4in : D'=-1+B, E'=A, [ 0>=B ], cost: 1
16.20/11.13	
16.20/11.13	      7: evalperfect2bb1in -> evalperfect2bb4in : D'=-1+B, E'=A, [ B>=2 ], cost: 1
16.20/11.13	
16.20/11.13	      8: evalperfect2bb2in -> evalperfect2bb3in : [ 0>=1+C ], cost: 1
16.20/11.13	
16.20/11.13	      9: evalperfect2bb2in -> evalperfect2bb3in : [ C>=1 ], cost: 1
16.20/11.13	
16.20/11.13	     10: evalperfect2bb2in -> evalperfect2bb3in : [ C==0 ], cost: 1
16.20/11.13	
16.20/11.13	     11: evalperfect2bb3in -> evalperfect2stop : [], cost: 1
16.20/11.13	
16.20/11.13	     12: evalperfect2bb4in -> evalperfect2bb5in : [ E>=D ], cost: 1
16.20/11.13	
16.20/11.13	     13: evalperfect2bb4in -> evalperfect2bb6in : [ D>=1+E ], cost: 1
16.20/11.13	
16.20/11.13	     14: evalperfect2bb5in -> evalperfect2bb4in : E'=-D+E, [], cost: 1
16.20/11.13	
16.20/11.13	     15: evalperfect2bb6in -> evalperfect29 : F'=C-D, [], cost: 1
16.20/11.13	
16.20/11.13	     16: evalperfect29 -> evalperfect210 : [], cost: 1
16.20/11.13	
16.20/11.13	     17: evalperfect210 -> evalperfect211 : G'=F, [ E==0 ], cost: 1
16.20/11.13	
16.20/11.13	     18: evalperfect210 -> evalperfect211 : G'=C, [ 0>=1+E ], cost: 1
16.20/11.13	
16.20/11.13	     19: evalperfect210 -> evalperfect211 : G'=C, [ E>=1 ], cost: 1
16.20/11.13	
16.20/11.13	     20: evalperfect211 -> evalperfect212 : [], cost: 1
16.20/11.13	
16.20/11.13	     21: evalperfect212 -> evalperfect2bb1in : B'=D, C'=G, [], cost: 1
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	Removed unreachable and leaf rules:
16.20/11.13	
16.20/11.13	   Start location: evalperfect2start
16.20/11.13	
16.20/11.13	      0: evalperfect2start -> evalperfect2bb0in : [], cost: 1
16.20/11.13	
16.20/11.13	      1: evalperfect2bb0in -> evalperfect20 : [], cost: 1
16.20/11.13	
16.20/11.13	      2: evalperfect20 -> evalperfect21 : [], cost: 1
16.20/11.13	
16.20/11.13	      4: evalperfect21 -> evalperfect2bb1in : B'=A, C'=A, [ A>=1 ], cost: 1
16.20/11.13	
16.20/11.13	      6: evalperfect2bb1in -> evalperfect2bb4in : D'=-1+B, E'=A, [ 0>=B ], cost: 1
16.20/11.13	
16.20/11.13	      7: evalperfect2bb1in -> evalperfect2bb4in : D'=-1+B, E'=A, [ B>=2 ], cost: 1
16.20/11.13	
16.20/11.13	     12: evalperfect2bb4in -> evalperfect2bb5in : [ E>=D ], cost: 1
16.20/11.13	
16.20/11.13	     13: evalperfect2bb4in -> evalperfect2bb6in : [ D>=1+E ], cost: 1
16.20/11.13	
16.20/11.13	     14: evalperfect2bb5in -> evalperfect2bb4in : E'=-D+E, [], cost: 1
16.20/11.13	
16.20/11.13	     15: evalperfect2bb6in -> evalperfect29 : F'=C-D, [], cost: 1
16.20/11.13	
16.20/11.13	     16: evalperfect29 -> evalperfect210 : [], cost: 1
16.20/11.13	
16.20/11.13	     17: evalperfect210 -> evalperfect211 : G'=F, [ E==0 ], cost: 1
16.20/11.13	
16.20/11.13	     18: evalperfect210 -> evalperfect211 : G'=C, [ 0>=1+E ], cost: 1
16.20/11.13	
16.20/11.13	     19: evalperfect210 -> evalperfect211 : G'=C, [ E>=1 ], cost: 1
16.20/11.13	
16.20/11.13	     20: evalperfect211 -> evalperfect212 : [], cost: 1
16.20/11.13	
16.20/11.13	     21: evalperfect212 -> evalperfect2bb1in : B'=D, C'=G, [], cost: 1
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	### Simplification by acceleration and chaining ###
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	Eliminated locations (on linear paths):
16.20/11.13	
16.20/11.13	   Start location: evalperfect2start
16.20/11.13	
16.20/11.13	     24: evalperfect2start -> evalperfect2bb1in : B'=A, C'=A, [ A>=1 ], cost: 4
16.20/11.13	
16.20/11.13	      6: evalperfect2bb1in -> evalperfect2bb4in : D'=-1+B, E'=A, [ 0>=B ], cost: 1
16.20/11.13	
16.20/11.13	      7: evalperfect2bb1in -> evalperfect2bb4in : D'=-1+B, E'=A, [ B>=2 ], cost: 1
16.20/11.13	
16.20/11.13	     25: evalperfect2bb4in -> evalperfect2bb4in : E'=-D+E, [ E>=D ], cost: 2
16.20/11.13	
16.20/11.13	     27: evalperfect2bb4in -> evalperfect210 : F'=C-D, [ D>=1+E ], cost: 3
16.20/11.13	
16.20/11.13	     17: evalperfect210 -> evalperfect211 : G'=F, [ E==0 ], cost: 1
16.20/11.13	
16.20/11.13	     18: evalperfect210 -> evalperfect211 : G'=C, [ 0>=1+E ], cost: 1
16.20/11.13	
16.20/11.13	     19: evalperfect210 -> evalperfect211 : G'=C, [ E>=1 ], cost: 1
16.20/11.13	
16.20/11.13	     28: evalperfect211 -> evalperfect2bb1in : B'=D, C'=G, [], cost: 2
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	Accelerating simple loops of location 7.
16.20/11.13	
16.20/11.13	   Accelerating the following rules:
16.20/11.13	
16.20/11.13	     25: evalperfect2bb4in -> evalperfect2bb4in : E'=-D+E, [ E>=D ], cost: 2
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	   Found no metering function for rule 25.
16.20/11.13	
16.20/11.13	   Removing the simple loops:.
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	Accelerated all simple loops using metering functions (where possible):
16.20/11.13	
16.20/11.13	   Start location: evalperfect2start
16.20/11.13	
16.20/11.13	     24: evalperfect2start -> evalperfect2bb1in : B'=A, C'=A, [ A>=1 ], cost: 4
16.20/11.13	
16.20/11.13	      6: evalperfect2bb1in -> evalperfect2bb4in : D'=-1+B, E'=A, [ 0>=B ], cost: 1
16.20/11.13	
16.20/11.13	      7: evalperfect2bb1in -> evalperfect2bb4in : D'=-1+B, E'=A, [ B>=2 ], cost: 1
16.20/11.13	
16.20/11.13	     25: evalperfect2bb4in -> evalperfect2bb4in : E'=-D+E, [ E>=D ], cost: 2
16.20/11.13	
16.20/11.13	     27: evalperfect2bb4in -> evalperfect210 : F'=C-D, [ D>=1+E ], cost: 3
16.20/11.13	
16.20/11.13	     17: evalperfect210 -> evalperfect211 : G'=F, [ E==0 ], cost: 1
16.20/11.13	
16.20/11.13	     18: evalperfect210 -> evalperfect211 : G'=C, [ 0>=1+E ], cost: 1
16.20/11.13	
16.20/11.13	     19: evalperfect210 -> evalperfect211 : G'=C, [ E>=1 ], cost: 1
16.20/11.13	
16.20/11.13	     28: evalperfect211 -> evalperfect2bb1in : B'=D, C'=G, [], cost: 2
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	Chained accelerated rules (with incoming rules):
16.20/11.13	
16.20/11.13	   Start location: evalperfect2start
16.20/11.13	
16.20/11.13	     24: evalperfect2start -> evalperfect2bb1in : B'=A, C'=A, [ A>=1 ], cost: 4
16.20/11.13	
16.20/11.13	      6: evalperfect2bb1in -> evalperfect2bb4in : D'=-1+B, E'=A, [ 0>=B ], cost: 1
16.20/11.13	
16.20/11.13	      7: evalperfect2bb1in -> evalperfect2bb4in : D'=-1+B, E'=A, [ B>=2 ], cost: 1
16.20/11.13	
16.20/11.13	     29: evalperfect2bb1in -> evalperfect2bb4in : D'=-1+B, E'=1+A-B, [ 0>=B && A>=-1+B ], cost: 3
16.20/11.13	
16.20/11.13	     30: evalperfect2bb1in -> evalperfect2bb4in : D'=-1+B, E'=1+A-B, [ B>=2 && A>=-1+B ], cost: 3
16.20/11.13	
16.20/11.13	     27: evalperfect2bb4in -> evalperfect210 : F'=C-D, [ D>=1+E ], cost: 3
16.20/11.13	
16.20/11.13	     17: evalperfect210 -> evalperfect211 : G'=F, [ E==0 ], cost: 1
16.20/11.13	
16.20/11.13	     18: evalperfect210 -> evalperfect211 : G'=C, [ 0>=1+E ], cost: 1
16.20/11.13	
16.20/11.13	     19: evalperfect210 -> evalperfect211 : G'=C, [ E>=1 ], cost: 1
16.20/11.13	
16.20/11.13	     28: evalperfect211 -> evalperfect2bb1in : B'=D, C'=G, [], cost: 2
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	Eliminated locations (on tree-shaped paths):
16.20/11.13	
16.20/11.13	   Start location: evalperfect2start
16.20/11.13	
16.20/11.13	     24: evalperfect2start -> evalperfect2bb1in : B'=A, C'=A, [ A>=1 ], cost: 4
16.20/11.13	
16.20/11.13	     31: evalperfect2bb1in -> evalperfect210 : D'=-1+B, E'=A, F'=1+C-B, [ 0>=B && -1+B>=1+A ], cost: 4
16.20/11.13	
16.20/11.13	     32: evalperfect2bb1in -> evalperfect210 : D'=-1+B, E'=A, F'=1+C-B, [ B>=2 && -1+B>=1+A ], cost: 4
16.20/11.13	
16.20/11.13	     33: evalperfect2bb1in -> evalperfect210 : D'=-1+B, E'=1+A-B, F'=1+C-B, [ B>=2 && A>=-1+B && -1+B>=2+A-B ], cost: 6
16.20/11.13	
16.20/11.13	     34: evalperfect210 -> evalperfect2bb1in : B'=D, C'=F, G'=F, [ E==0 ], cost: 3
16.20/11.13	
16.20/11.13	     35: evalperfect210 -> evalperfect2bb1in : B'=D, C'=C, G'=C, [ 0>=1+E ], cost: 3
16.20/11.13	
16.20/11.13	     36: evalperfect210 -> evalperfect2bb1in : B'=D, C'=C, G'=C, [ E>=1 ], cost: 3
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	Eliminated locations (on tree-shaped paths):
16.20/11.13	
16.20/11.13	   Start location: evalperfect2start
16.20/11.13	
16.20/11.13	     24: evalperfect2start -> evalperfect2bb1in : B'=A, C'=A, [ A>=1 ], cost: 4
16.20/11.13	
16.20/11.13	     37: evalperfect2bb1in -> evalperfect2bb1in : B'=-1+B, C'=C, D'=-1+B, E'=A, F'=1+C-B, G'=C, [ 0>=B && -1+B>=1+A && 0>=1+A ], cost: 7
16.20/11.13	
16.20/11.13	     38: evalperfect2bb1in -> evalperfect2bb1in : 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: 7
16.20/11.13	
16.20/11.13	     39: evalperfect2bb1in -> evalperfect2bb1in : 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: 7
16.20/11.13	
16.20/11.13	     40: evalperfect2bb1in -> evalperfect2bb1in : 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: 7
16.20/11.13	
16.20/11.13	     41: evalperfect2bb1in -> evalperfect2bb1in : 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: 9
16.20/11.13	
16.20/11.13	     42: evalperfect2bb1in -> evalperfect2bb1in : 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: 9
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	Applied pruning (of leafs and parallel rules):
16.20/11.13	
16.20/11.13	   Start location: evalperfect2start
16.20/11.13	
16.20/11.13	     24: evalperfect2start -> evalperfect2bb1in : B'=A, C'=A, [ A>=1 ], cost: 4
16.20/11.13	
16.20/11.13	     37: evalperfect2bb1in -> evalperfect2bb1in : B'=-1+B, C'=C, D'=-1+B, E'=A, F'=1+C-B, G'=C, [ 0>=B && -1+B>=1+A && 0>=1+A ], cost: 7
16.20/11.13	
16.20/11.13	     38: evalperfect2bb1in -> evalperfect2bb1in : 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: 7
16.20/11.13	
16.20/11.13	     39: evalperfect2bb1in -> evalperfect2bb1in : 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: 7
16.20/11.13	
16.20/11.13	     40: evalperfect2bb1in -> evalperfect2bb1in : 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: 7
16.20/11.13	
16.20/11.13	     42: evalperfect2bb1in -> evalperfect2bb1in : 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: 9
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	Accelerating simple loops of location 4.
16.20/11.13	
16.20/11.13	   Simplified some of the simple loops (and removed duplicate rules).
16.20/11.13	
16.20/11.13	   Accelerating the following rules:
16.20/11.13	
16.20/11.13	     37: evalperfect2bb1in -> evalperfect2bb1in : B'=-1+B, D'=-1+B, E'=A, F'=1+C-B, G'=C, [ 0>=B && -1+B>=1+A && 0>=1+A ], cost: 7
16.20/11.13	
16.20/11.13	     38: evalperfect2bb1in -> evalperfect2bb1in : 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: 7
16.20/11.13	
16.20/11.13	     39: evalperfect2bb1in -> evalperfect2bb1in : B'=-1+B, D'=-1+B, E'=A, F'=1+C-B, G'=C, [ B>=2 && -1+B>=1+A && 0>=1+A ], cost: 7
16.20/11.13	
16.20/11.13	     40: evalperfect2bb1in -> evalperfect2bb1in : B'=-1+B, D'=-1+B, E'=A, F'=1+C-B, G'=C, [ B>=2 && -1+B>=1+A && A>=1 ], cost: 7
16.20/11.13	
16.20/11.13	     42: evalperfect2bb1in -> evalperfect2bb1in : 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: 9
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	   Accelerated rule 37 with metering function -1-A+B, yielding the new rule 43.
16.20/11.13	
16.20/11.13	   Accelerated rule 38 with metering function -1-A+B, yielding the new rule 44.
16.20/11.13	
16.20/11.13	   Accelerated rule 39 with metering function -1+B, yielding the new rule 45.
16.20/11.13	
16.20/11.13	   Accelerated rule 40 with metering function -1-A+B, yielding the new rule 46.
16.20/11.13	
16.20/11.13	   Accelerated rule 42 with metering function meter (where 2*meter==-2-A+2*B), yielding the new rule 47.
16.20/11.13	
16.20/11.13	   Removing the simple loops: 37 38 39 40 42.
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	Accelerated all simple loops using metering functions (where possible):
16.20/11.13	
16.20/11.13	   Start location: evalperfect2start
16.20/11.13	
16.20/11.13	     24: evalperfect2start -> evalperfect2bb1in : B'=A, C'=A, [ A>=1 ], cost: 4
16.20/11.13	
16.20/11.13	     43: evalperfect2bb1in -> evalperfect2bb1in : B'=1+A, D'=1+A, E'=A, F'=-1+C-A, G'=C, [ 0>=B && -1+B>=1+A && 0>=1+A ], cost: -7-7*A+7*B
16.20/11.13	
16.20/11.13	     44: evalperfect2bb1in -> evalperfect2bb1in : 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: -7-7*A+7*B
16.20/11.13	
16.20/11.13	     45: evalperfect2bb1in -> evalperfect2bb1in : B'=1, D'=1, E'=A, F'=-1+C, G'=C, [ B>=2 && -1+B>=1+A && 0>=1+A ], cost: -7+7*B
16.20/11.13	
16.20/11.13	     46: evalperfect2bb1in -> evalperfect2bb1in : B'=1+A, D'=1+A, E'=A, F'=-1+C-A, G'=C, [ B>=2 && -1+B>=1+A && A>=1 ], cost: -7-7*A+7*B
16.20/11.13	
16.20/11.13	     47: evalperfect2bb1in -> evalperfect2bb1in : B'=-meter+B, D'=-meter+B, E'=meter+A-B, F'=C+meter-B, G'=C, [ B>=2 && -1+B>=2+A-B && 1+A-B>=1 && 2*meter==-2-A+2*B && meter>=1 ], cost: 9*meter
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	Chained accelerated rules (with incoming rules):
16.20/11.13	
16.20/11.13	   Start location: evalperfect2start
16.20/11.13	
16.20/11.13	     24: evalperfect2start -> evalperfect2bb1in : B'=A, C'=A, [ A>=1 ], cost: 4
16.20/11.13	
16.20/11.13	     48: evalperfect2start -> evalperfect2bb1in : 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+9*meter
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	Removed unreachable locations (and leaf rules with constant cost):
16.20/11.13	
16.20/11.13	   Start location: evalperfect2start
16.20/11.13	
16.20/11.13	     48: evalperfect2start -> evalperfect2bb1in : 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+9*meter
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	### Computing asymptotic complexity ###
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	Fully simplified ITS problem
16.20/11.13	
16.20/11.13	   Start location: evalperfect2start
16.20/11.13	
16.20/11.13	     48: evalperfect2start -> evalperfect2bb1in : 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+9*meter
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	Computing asymptotic complexity for rule 48
16.20/11.13	
16.20/11.13	   Solved the limit problem by the following transformations:
16.20/11.13	
16.20/11.13	      Created initial limit problem:
16.20/11.13	
16.20/11.13	      3+2*meter-A (+/+!), -1-2*meter+A (+/+!), 4+9*meter (+), -2+A (+/+!) [not solved]
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	      applying transformation rule (C) using substitution {A==2+2*meter}
16.20/11.13	
16.20/11.13	      resulting limit problem:
16.20/11.13	
16.20/11.13	      1 (+/+!), 2*meter (+/+!), 4+9*meter (+) [not solved]
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	      applying transformation rule (B), deleting 1 (+/+!)
16.20/11.13	
16.20/11.13	      resulting limit problem:
16.20/11.13	
16.20/11.13	      2*meter (+/+!), 4+9*meter (+) [not solved]
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	      removing all constraints (solved by SMT)
16.20/11.13	
16.20/11.13	      resulting limit problem: [solved]
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	      applying transformation rule (C) using substitution {meter==n}
16.20/11.13	
16.20/11.13	      resulting limit problem:
16.20/11.13	
16.20/11.13	      [solved]
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	   Solved the limit problem by the following transformations:
16.20/11.13	
16.20/11.13	      Created initial limit problem:
16.20/11.13	
16.20/11.13	      3+2*meter-A (+/+!), -1-2*meter+A (+/+!), 4+9*meter (+), -2+A (+/+!) [not solved]
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	      applying transformation rule (C) using substitution {A==2+2*meter}
16.20/11.13	
16.20/11.13	      resulting limit problem:
16.20/11.13	
16.20/11.13	      1 (+/+!), 2*meter (+/+!), 4+9*meter (+) [not solved]
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	      applying transformation rule (B), deleting 1 (+/+!)
16.20/11.13	
16.20/11.13	      resulting limit problem:
16.20/11.13	
16.20/11.13	      2*meter (+/+!), 4+9*meter (+) [not solved]
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	      removing all constraints (solved by SMT)
16.20/11.13	
16.20/11.13	      resulting limit problem: [solved]
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	      applying transformation rule (C) using substitution {meter==n}
16.20/11.13	
16.20/11.13	      resulting limit problem:
16.20/11.13	
16.20/11.13	      [solved]
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	   Solution:
16.20/11.13	
16.20/11.13	      meter / n
16.20/11.13	
16.20/11.13	      A / 2+2*n
16.20/11.13	
16.20/11.13	   Resulting cost 4+9*n has complexity: Poly(n^1)
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	Found new complexity Poly(n^1).
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	Obtained the following overall complexity (w.r.t. the length of the input n):
16.20/11.13	
16.20/11.13	   Complexity:  Poly(n^1)
16.20/11.13	
16.20/11.13	   Cpx degree:  1
16.20/11.13	
16.20/11.13	   Solved cost: 4+9*n
16.20/11.13	
16.20/11.13	   Rule cost:   4+9*meter
16.20/11.13	
16.20/11.13	   Rule guard:  [ -1+A>=2 && 2*meter==-2+A ]
16.20/11.13	
16.20/11.13	
16.20/11.13	
16.20/11.13	WORST_CASE(Omega(n^1),?)
16.20/11.13	
16.20/11.13	
16.20/11.13	----------------------------------------
16.20/11.13	
16.20/11.13	(2)
16.20/11.13	BOUNDS(n^1, INF)
16.40/11.16	EOF