16.11/10.94	WORST_CASE(Omega(n^1), O(n^2))
16.11/10.96	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
16.11/10.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
16.11/10.96	
16.11/10.96	
16.11/10.96	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(7, 7 + Arg_0 * max(6, 3 * Arg_0)) + nat(Arg_0 * max(6, 3 * Arg_0)) * nat(Arg_0) + max(3, 3 * Arg_0) * nat(Arg_0) + max(3, 3 * Arg_0) + nat(6 * Arg_0) + nat(2 * Arg_0) + max(3, 3 + Arg_0)).
16.11/10.96	
16.11/10.96	(0) CpxIntTrs
16.11/10.96	(1) Loat Proof [FINISHED, 1853 ms]
16.11/10.96	(2) BOUNDS(n^1, INF)
16.11/10.96	
16.11/10.96	
16.11/10.96	----------------------------------------
16.11/10.96	
16.11/10.96	(0)
16.11/10.96	Obligation:
16.11/10.96	Complexity Int TRS consisting of the following rules:
16.11/10.96	eval_unperfect_start(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_bb0_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE
16.11/10.96	eval_unperfect_bb0_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_0(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE
16.11/10.96	eval_unperfect_0(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_1(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE
16.11/10.96	eval_unperfect_1(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_bb3_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_x <= 0
16.11/10.96	eval_unperfect_1(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_bb1_in(v__y3_0, v_1, v_8, v_x, v_x, v_y2_1, v_x)) :|: v_x > 0
16.11/10.96	eval_unperfect_bb1_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_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
16.11/10.96	eval_unperfect_bb1_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_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
16.11/10.96	eval_unperfect_bb1_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_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
16.11/10.96	eval_unperfect_bb2_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_bb3_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y3_0 < 0
16.11/10.96	eval_unperfect_bb2_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_bb3_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y3_0 > 0
16.11/10.96	eval_unperfect_bb2_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_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
16.11/10.96	eval_unperfect_bb3_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_stop(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE
16.11/10.96	eval_unperfect_bb4_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_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
16.11/10.96	eval_unperfect_bb4_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_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
16.11/10.96	eval_unperfect_bb5_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_bb4_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1 - v_1, v_y3_0)) :|: TRUE
16.11/10.96	eval_unperfect_bb6_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_9(v__y3_0, v_1, v_y3_0 - v_1, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE
16.11/10.96	eval_unperfect_9(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_10(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE
16.11/10.96	eval_unperfect_10(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_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
16.11/10.96	eval_unperfect_10(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_11(v_y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y2_1 < 0
16.11/10.96	eval_unperfect_10(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_11(v_y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y2_1 > 0
16.11/10.96	eval_unperfect_11(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_12(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE
16.11/10.96	eval_unperfect_12(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_unperfect_bb1_in(v__y3_0, v_1, v_8, v_x, v_1, v_y2_1, v__y3_0)) :|: TRUE
16.11/10.96	
16.11/10.96	The start-symbols are:[eval_unperfect_start_7]
16.11/10.96	
16.11/10.96	
16.11/10.96	----------------------------------------
16.11/10.96	
16.11/10.96	(1) Loat Proof (FINISHED)
16.11/10.96	
16.11/10.96	
16.11/10.96	### Pre-processing the ITS problem ###
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	Initial linear ITS problem
16.11/10.96	
16.11/10.96	   Start location: evalunperfectstart
16.11/10.96	
16.11/10.96	      0: evalunperfectstart -> evalunperfectbb0in : [], cost: 1
16.11/10.96	
16.11/10.96	      1: evalunperfectbb0in -> evalunperfect0 : [], cost: 1
16.11/10.96	
16.11/10.96	      2: evalunperfect0 -> evalunperfect1 : [], cost: 1
16.11/10.96	
16.11/10.96	      3: evalunperfect1 -> evalunperfectbb3in : [ 0>=A ], cost: 1
16.11/10.96	
16.11/10.96	      4: evalunperfect1 -> evalunperfectbb1in : B'=A, C'=A, [ A>=1 ], cost: 1
16.11/10.96	
16.11/10.96	      5: evalunperfectbb1in -> evalunperfectbb2in : [ B==1 ], cost: 1
16.11/10.96	
16.11/10.96	      6: evalunperfectbb1in -> evalunperfectbb4in : D'=-1+B, E'=A, [ 0>=B ], cost: 1
16.11/10.96	
16.11/10.96	      7: evalunperfectbb1in -> evalunperfectbb4in : D'=-1+B, E'=A, [ B>=2 ], cost: 1
16.11/10.96	
16.11/10.96	      8: evalunperfectbb2in -> evalunperfectbb3in : [ 0>=1+C ], cost: 1
16.11/10.96	
16.11/10.96	      9: evalunperfectbb2in -> evalunperfectbb3in : [ C>=1 ], cost: 1
16.11/10.96	
16.11/10.96	     10: evalunperfectbb2in -> evalunperfectbb3in : [ C==0 ], cost: 1
16.11/10.96	
16.11/10.96	     11: evalunperfectbb3in -> evalunperfectstop : [], cost: 1
16.11/10.96	
16.11/10.96	     12: evalunperfectbb4in -> evalunperfectbb5in : [ E>=D ], cost: 1
16.11/10.96	
16.11/10.96	     13: evalunperfectbb4in -> evalunperfectbb6in : [ D>=1+E ], cost: 1
16.11/10.96	
16.11/10.96	     14: evalunperfectbb5in -> evalunperfectbb4in : E'=-D+E, [], cost: 1
16.11/10.96	
16.11/10.96	     15: evalunperfectbb6in -> evalunperfect9 : F'=C-D, [], cost: 1
16.11/10.96	
16.11/10.96	     16: evalunperfect9 -> evalunperfect10 : [], cost: 1
16.11/10.96	
16.11/10.96	     17: evalunperfect10 -> evalunperfect11 : G'=F, [ E==0 ], cost: 1
16.11/10.96	
16.11/10.96	     18: evalunperfect10 -> evalunperfect11 : G'=C, [ 0>=1+E ], cost: 1
16.11/10.96	
16.11/10.96	     19: evalunperfect10 -> evalunperfect11 : G'=C, [ E>=1 ], cost: 1
16.11/10.96	
16.11/10.96	     20: evalunperfect11 -> evalunperfect12 : [], cost: 1
16.11/10.96	
16.11/10.96	     21: evalunperfect12 -> evalunperfectbb1in : B'=D, C'=G, [], cost: 1
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	Removed unreachable and leaf rules:
16.11/10.96	
16.11/10.96	   Start location: evalunperfectstart
16.11/10.96	
16.11/10.96	      0: evalunperfectstart -> evalunperfectbb0in : [], cost: 1
16.11/10.96	
16.11/10.96	      1: evalunperfectbb0in -> evalunperfect0 : [], cost: 1
16.11/10.96	
16.11/10.96	      2: evalunperfect0 -> evalunperfect1 : [], cost: 1
16.11/10.96	
16.11/10.96	      4: evalunperfect1 -> evalunperfectbb1in : B'=A, C'=A, [ A>=1 ], cost: 1
16.11/10.96	
16.11/10.96	      6: evalunperfectbb1in -> evalunperfectbb4in : D'=-1+B, E'=A, [ 0>=B ], cost: 1
16.11/10.96	
16.11/10.96	      7: evalunperfectbb1in -> evalunperfectbb4in : D'=-1+B, E'=A, [ B>=2 ], cost: 1
16.11/10.96	
16.11/10.96	     12: evalunperfectbb4in -> evalunperfectbb5in : [ E>=D ], cost: 1
16.11/10.96	
16.11/10.96	     13: evalunperfectbb4in -> evalunperfectbb6in : [ D>=1+E ], cost: 1
16.11/10.96	
16.11/10.96	     14: evalunperfectbb5in -> evalunperfectbb4in : E'=-D+E, [], cost: 1
16.11/10.96	
16.11/10.96	     15: evalunperfectbb6in -> evalunperfect9 : F'=C-D, [], cost: 1
16.11/10.96	
16.11/10.96	     16: evalunperfect9 -> evalunperfect10 : [], cost: 1
16.11/10.96	
16.11/10.96	     17: evalunperfect10 -> evalunperfect11 : G'=F, [ E==0 ], cost: 1
16.11/10.96	
16.11/10.96	     18: evalunperfect10 -> evalunperfect11 : G'=C, [ 0>=1+E ], cost: 1
16.11/10.96	
16.11/10.96	     19: evalunperfect10 -> evalunperfect11 : G'=C, [ E>=1 ], cost: 1
16.11/10.96	
16.11/10.96	     20: evalunperfect11 -> evalunperfect12 : [], cost: 1
16.11/10.96	
16.11/10.96	     21: evalunperfect12 -> evalunperfectbb1in : B'=D, C'=G, [], cost: 1
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	### Simplification by acceleration and chaining ###
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	Eliminated locations (on linear paths):
16.11/10.96	
16.11/10.96	   Start location: evalunperfectstart
16.11/10.96	
16.11/10.96	     24: evalunperfectstart -> evalunperfectbb1in : B'=A, C'=A, [ A>=1 ], cost: 4
16.11/10.96	
16.11/10.96	      6: evalunperfectbb1in -> evalunperfectbb4in : D'=-1+B, E'=A, [ 0>=B ], cost: 1
16.11/10.96	
16.11/10.96	      7: evalunperfectbb1in -> evalunperfectbb4in : D'=-1+B, E'=A, [ B>=2 ], cost: 1
16.11/10.96	
16.11/10.96	     25: evalunperfectbb4in -> evalunperfectbb4in : E'=-D+E, [ E>=D ], cost: 2
16.11/10.96	
16.11/10.96	     27: evalunperfectbb4in -> evalunperfect10 : F'=C-D, [ D>=1+E ], cost: 3
16.11/10.96	
16.11/10.96	     17: evalunperfect10 -> evalunperfect11 : G'=F, [ E==0 ], cost: 1
16.11/10.96	
16.11/10.96	     18: evalunperfect10 -> evalunperfect11 : G'=C, [ 0>=1+E ], cost: 1
16.11/10.96	
16.11/10.96	     19: evalunperfect10 -> evalunperfect11 : G'=C, [ E>=1 ], cost: 1
16.11/10.96	
16.11/10.96	     28: evalunperfect11 -> evalunperfectbb1in : B'=D, C'=G, [], cost: 2
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	Accelerating simple loops of location 7.
16.11/10.96	
16.11/10.96	   Accelerating the following rules:
16.11/10.96	
16.11/10.96	     25: evalunperfectbb4in -> evalunperfectbb4in : E'=-D+E, [ E>=D ], cost: 2
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	   Found no metering function for rule 25.
16.11/10.96	
16.11/10.96	   Removing the simple loops:.
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	Accelerated all simple loops using metering functions (where possible):
16.11/10.96	
16.11/10.96	   Start location: evalunperfectstart
16.11/10.96	
16.11/10.96	     24: evalunperfectstart -> evalunperfectbb1in : B'=A, C'=A, [ A>=1 ], cost: 4
16.11/10.96	
16.11/10.96	      6: evalunperfectbb1in -> evalunperfectbb4in : D'=-1+B, E'=A, [ 0>=B ], cost: 1
16.11/10.96	
16.11/10.96	      7: evalunperfectbb1in -> evalunperfectbb4in : D'=-1+B, E'=A, [ B>=2 ], cost: 1
16.11/10.96	
16.11/10.96	     25: evalunperfectbb4in -> evalunperfectbb4in : E'=-D+E, [ E>=D ], cost: 2
16.11/10.96	
16.11/10.96	     27: evalunperfectbb4in -> evalunperfect10 : F'=C-D, [ D>=1+E ], cost: 3
16.11/10.96	
16.11/10.96	     17: evalunperfect10 -> evalunperfect11 : G'=F, [ E==0 ], cost: 1
16.11/10.96	
16.11/10.96	     18: evalunperfect10 -> evalunperfect11 : G'=C, [ 0>=1+E ], cost: 1
16.11/10.96	
16.11/10.96	     19: evalunperfect10 -> evalunperfect11 : G'=C, [ E>=1 ], cost: 1
16.11/10.96	
16.11/10.96	     28: evalunperfect11 -> evalunperfectbb1in : B'=D, C'=G, [], cost: 2
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	Chained accelerated rules (with incoming rules):
16.11/10.96	
16.11/10.96	   Start location: evalunperfectstart
16.11/10.96	
16.11/10.96	     24: evalunperfectstart -> evalunperfectbb1in : B'=A, C'=A, [ A>=1 ], cost: 4
16.11/10.96	
16.11/10.96	      6: evalunperfectbb1in -> evalunperfectbb4in : D'=-1+B, E'=A, [ 0>=B ], cost: 1
16.11/10.96	
16.11/10.96	      7: evalunperfectbb1in -> evalunperfectbb4in : D'=-1+B, E'=A, [ B>=2 ], cost: 1
16.11/10.96	
16.11/10.96	     29: evalunperfectbb1in -> evalunperfectbb4in : D'=-1+B, E'=1+A-B, [ 0>=B && A>=-1+B ], cost: 3
16.11/10.96	
16.11/10.96	     30: evalunperfectbb1in -> evalunperfectbb4in : D'=-1+B, E'=1+A-B, [ B>=2 && A>=-1+B ], cost: 3
16.11/10.96	
16.11/10.96	     27: evalunperfectbb4in -> evalunperfect10 : F'=C-D, [ D>=1+E ], cost: 3
16.11/10.96	
16.11/10.96	     17: evalunperfect10 -> evalunperfect11 : G'=F, [ E==0 ], cost: 1
16.11/10.96	
16.11/10.96	     18: evalunperfect10 -> evalunperfect11 : G'=C, [ 0>=1+E ], cost: 1
16.11/10.96	
16.11/10.96	     19: evalunperfect10 -> evalunperfect11 : G'=C, [ E>=1 ], cost: 1
16.11/10.96	
16.11/10.96	     28: evalunperfect11 -> evalunperfectbb1in : B'=D, C'=G, [], cost: 2
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	Eliminated locations (on tree-shaped paths):
16.11/10.96	
16.11/10.96	   Start location: evalunperfectstart
16.11/10.96	
16.11/10.96	     24: evalunperfectstart -> evalunperfectbb1in : B'=A, C'=A, [ A>=1 ], cost: 4
16.11/10.96	
16.11/10.96	     31: evalunperfectbb1in -> evalunperfect10 : D'=-1+B, E'=A, F'=1+C-B, [ 0>=B && -1+B>=1+A ], cost: 4
16.11/10.96	
16.11/10.96	     32: evalunperfectbb1in -> evalunperfect10 : D'=-1+B, E'=A, F'=1+C-B, [ B>=2 && -1+B>=1+A ], cost: 4
16.11/10.96	
16.11/10.96	     33: evalunperfectbb1in -> evalunperfect10 : D'=-1+B, E'=1+A-B, F'=1+C-B, [ B>=2 && A>=-1+B && -1+B>=2+A-B ], cost: 6
16.11/10.96	
16.11/10.96	     34: evalunperfect10 -> evalunperfectbb1in : B'=D, C'=F, G'=F, [ E==0 ], cost: 3
16.11/10.96	
16.11/10.96	     35: evalunperfect10 -> evalunperfectbb1in : B'=D, C'=C, G'=C, [ 0>=1+E ], cost: 3
16.11/10.96	
16.11/10.96	     36: evalunperfect10 -> evalunperfectbb1in : B'=D, C'=C, G'=C, [ E>=1 ], cost: 3
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	Eliminated locations (on tree-shaped paths):
16.11/10.96	
16.11/10.96	   Start location: evalunperfectstart
16.11/10.96	
16.11/10.96	     24: evalunperfectstart -> evalunperfectbb1in : B'=A, C'=A, [ A>=1 ], cost: 4
16.11/10.96	
16.11/10.96	     37: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	     38: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	     39: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	     40: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	     41: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	     42: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	Applied pruning (of leafs and parallel rules):
16.11/10.96	
16.11/10.96	   Start location: evalunperfectstart
16.11/10.96	
16.11/10.96	     24: evalunperfectstart -> evalunperfectbb1in : B'=A, C'=A, [ A>=1 ], cost: 4
16.11/10.96	
16.11/10.96	     37: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	     38: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	     39: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	     40: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	     42: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	Accelerating simple loops of location 4.
16.11/10.96	
16.11/10.96	   Simplified some of the simple loops (and removed duplicate rules).
16.11/10.96	
16.11/10.96	   Accelerating the following rules:
16.11/10.96	
16.11/10.96	     37: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	     38: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	     39: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	     40: evalunperfectbb1in -> evalunperfectbb1in : B'=-1+B, D'=-1+B, E'=A, F'=1+C-B, G'=C, [ B>=2 && -1+B>=1+A && A>=1 ], cost: 7
16.11/10.96	
16.11/10.96	     42: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	   Accelerated rule 37 with metering function -1-A+B, yielding the new rule 43.
16.11/10.96	
16.11/10.96	   Accelerated rule 38 with metering function -1-A+B, yielding the new rule 44.
16.11/10.96	
16.11/10.96	   Accelerated rule 39 with metering function -1+B, yielding the new rule 45.
16.11/10.96	
16.11/10.96	   Accelerated rule 40 with metering function -1-A+B, yielding the new rule 46.
16.11/10.96	
16.11/10.96	   Accelerated rule 42 with metering function meter (where 2*meter==-2-A+2*B), yielding the new rule 47.
16.11/10.96	
16.11/10.96	   Removing the simple loops: 37 38 39 40 42.
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	Accelerated all simple loops using metering functions (where possible):
16.11/10.96	
16.11/10.96	   Start location: evalunperfectstart
16.11/10.96	
16.11/10.96	     24: evalunperfectstart -> evalunperfectbb1in : B'=A, C'=A, [ A>=1 ], cost: 4
16.11/10.96	
16.11/10.96	     43: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	     44: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	     45: evalunperfectbb1in -> evalunperfectbb1in : B'=1, D'=1, E'=A, F'=-1+C, G'=C, [ B>=2 && -1+B>=1+A && 0>=1+A ], cost: -7+7*B
16.11/10.96	
16.11/10.96	     46: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	     47: evalunperfectbb1in -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	Chained accelerated rules (with incoming rules):
16.11/10.96	
16.11/10.96	   Start location: evalunperfectstart
16.11/10.96	
16.11/10.96	     24: evalunperfectstart -> evalunperfectbb1in : B'=A, C'=A, [ A>=1 ], cost: 4
16.11/10.96	
16.11/10.96	     48: evalunperfectstart -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	Removed unreachable locations (and leaf rules with constant cost):
16.11/10.96	
16.11/10.96	   Start location: evalunperfectstart
16.11/10.96	
16.11/10.96	     48: evalunperfectstart -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	### Computing asymptotic complexity ###
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	Fully simplified ITS problem
16.11/10.96	
16.11/10.96	   Start location: evalunperfectstart
16.11/10.96	
16.11/10.96	     48: evalunperfectstart -> evalunperfectbb1in : 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
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	Computing asymptotic complexity for rule 48
16.11/10.96	
16.11/10.96	   Solved the limit problem by the following transformations:
16.11/10.96	
16.11/10.96	      Created initial limit problem:
16.11/10.96	
16.11/10.96	      3+2*meter-A (+/+!), -1-2*meter+A (+/+!), 4+9*meter (+), -2+A (+/+!) [not solved]
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	      applying transformation rule (C) using substitution {A==2+2*meter}
16.11/10.96	
16.11/10.96	      resulting limit problem:
16.11/10.96	
16.11/10.96	      1 (+/+!), 2*meter (+/+!), 4+9*meter (+) [not solved]
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	      applying transformation rule (B), deleting 1 (+/+!)
16.11/10.96	
16.11/10.96	      resulting limit problem:
16.11/10.96	
16.11/10.96	      2*meter (+/+!), 4+9*meter (+) [not solved]
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	      removing all constraints (solved by SMT)
16.11/10.96	
16.11/10.96	      resulting limit problem: [solved]
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	      applying transformation rule (C) using substitution {meter==n}
16.11/10.96	
16.11/10.96	      resulting limit problem:
16.11/10.96	
16.11/10.96	      [solved]
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	   Solved the limit problem by the following transformations:
16.11/10.96	
16.11/10.96	      Created initial limit problem:
16.11/10.96	
16.11/10.96	      3+2*meter-A (+/+!), -1-2*meter+A (+/+!), 4+9*meter (+), -2+A (+/+!) [not solved]
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	      applying transformation rule (C) using substitution {A==2+2*meter}
16.11/10.96	
16.11/10.96	      resulting limit problem:
16.11/10.96	
16.11/10.96	      1 (+/+!), 2*meter (+/+!), 4+9*meter (+) [not solved]
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	      applying transformation rule (B), deleting 1 (+/+!)
16.11/10.96	
16.11/10.96	      resulting limit problem:
16.11/10.96	
16.11/10.96	      2*meter (+/+!), 4+9*meter (+) [not solved]
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	      removing all constraints (solved by SMT)
16.11/10.96	
16.11/10.96	      resulting limit problem: [solved]
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	      applying transformation rule (C) using substitution {meter==n}
16.11/10.96	
16.11/10.96	      resulting limit problem:
16.11/10.96	
16.11/10.96	      [solved]
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	   Solution:
16.11/10.96	
16.11/10.96	      meter / n
16.11/10.96	
16.11/10.96	      A / 2+2*n
16.11/10.96	
16.11/10.96	   Resulting cost 4+9*n has complexity: Poly(n^1)
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	Found new complexity Poly(n^1).
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	Obtained the following overall complexity (w.r.t. the length of the input n):
16.11/10.96	
16.11/10.96	   Complexity:  Poly(n^1)
16.11/10.96	
16.11/10.96	   Cpx degree:  1
16.11/10.96	
16.11/10.96	   Solved cost: 4+9*n
16.11/10.96	
16.11/10.96	   Rule cost:   4+9*meter
16.11/10.96	
16.11/10.96	   Rule guard:  [ -1+A>=2 && 2*meter==-2+A ]
16.11/10.96	
16.11/10.96	
16.11/10.96	
16.11/10.96	WORST_CASE(Omega(n^1),?)
16.11/10.96	
16.11/10.96	
16.11/10.96	----------------------------------------
16.11/10.96	
16.11/10.96	(2)
16.11/10.96	BOUNDS(n^1, INF)
16.22/10.99	EOF