15.68/10.30 MAYBE 15.69/10.31 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 15.69/10.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 15.69/10.31 15.69/10.31 15.69/10.31 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF). 15.69/10.31 15.69/10.31 (0) CpxIntTrs 15.69/10.31 (1) Loat Proof [FINISHED, 2661 ms] 15.69/10.31 (2) BOUNDS(1, INF) 15.69/10.31 15.69/10.31 15.69/10.31 ---------------------------------------- 15.69/10.31 15.69/10.31 (0) 15.69/10.31 Obligation: 15.69/10.31 Complexity Int TRS consisting of the following rules: 15.69/10.31 f0(A, B, C, D, E, F) -> Com_1(f8(1, 1, 0, 1, 1, F)) :|: TRUE 15.69/10.31 f8(A, B, C, D, E, F) -> Com_1(f10(A, B, C, D, E, F)) :|: 29 >= D 15.69/10.31 f10(A, B, C, D, E, F) -> Com_1(f14(A, B, C, D, G, F)) :|: D >= E + 1 && E >= 6 15.69/10.31 f10(A, B, C, D, E, F) -> Com_1(f14(A, B, C, D, E + 2, F)) :|: D >= E + 1 && 5 >= E 15.69/10.31 f14(A, B, C, D, E, F) -> Com_1(f10(A, B, C, D + 10, E, F)) :|: 12 >= E && E >= 10 15.69/10.31 f14(A, B, C, D, E, F) -> Com_1(f10(A, B, C, D + 1, E, F)) :|: E >= 13 15.69/10.31 f14(A, B, C, D, E, F) -> Com_1(f10(A, B, C, D + 1, E, F)) :|: 9 >= E 15.69/10.31 f10(A, B, C, D, E, F) -> Com_1(f8(A, B, C, D + 2, E - 10, F)) :|: E >= D 15.69/10.31 f8(A, B, C, D, E, F) -> Com_1(f28(A, B, 1, D, E, 1)) :|: D >= 30 15.69/10.31 15.69/10.31 The start-symbols are:[f0_6] 15.69/10.31 15.69/10.31 15.69/10.31 ---------------------------------------- 15.69/10.31 15.69/10.31 (1) Loat Proof (FINISHED) 15.69/10.31 15.69/10.31 15.69/10.31 ### Pre-processing the ITS problem ### 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 Initial linear ITS problem 15.69/10.31 15.69/10.31 Start location: f0 15.69/10.31 15.69/10.31 0: f0 -> f8 : A'=1, B'=1, C'=0, D'=1, E'=1, [], cost: 1 15.69/10.31 15.69/10.31 1: f8 -> f10 : [ 29>=D ], cost: 1 15.69/10.31 15.69/10.31 8: f8 -> f28 : C'=1, F'=1, [ D>=30 ], cost: 1 15.69/10.31 15.69/10.31 2: f10 -> f14 : E'=free, [ D>=1+E && E>=6 ], cost: 1 15.69/10.31 15.69/10.31 3: f10 -> f14 : E'=2+E, [ D>=1+E && 5>=E ], cost: 1 15.69/10.31 15.69/10.31 7: f10 -> f8 : D'=2+D, E'=-10+E, [ E>=D ], cost: 1 15.69/10.31 15.69/10.31 4: f14 -> f10 : D'=10+D, [ 12>=E && E>=10 ], cost: 1 15.69/10.31 15.69/10.31 5: f14 -> f10 : D'=1+D, [ E>=13 ], cost: 1 15.69/10.31 15.69/10.31 6: f14 -> f10 : D'=1+D, [ 9>=E ], cost: 1 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 Removed unreachable and leaf rules: 15.69/10.31 15.69/10.31 Start location: f0 15.69/10.31 15.69/10.31 0: f0 -> f8 : A'=1, B'=1, C'=0, D'=1, E'=1, [], cost: 1 15.69/10.31 15.69/10.31 1: f8 -> f10 : [ 29>=D ], cost: 1 15.69/10.31 15.69/10.31 2: f10 -> f14 : E'=free, [ D>=1+E && E>=6 ], cost: 1 15.69/10.31 15.69/10.31 3: f10 -> f14 : E'=2+E, [ D>=1+E && 5>=E ], cost: 1 15.69/10.31 15.69/10.31 7: f10 -> f8 : D'=2+D, E'=-10+E, [ E>=D ], cost: 1 15.69/10.31 15.69/10.31 4: f14 -> f10 : D'=10+D, [ 12>=E && E>=10 ], cost: 1 15.69/10.31 15.69/10.31 5: f14 -> f10 : D'=1+D, [ E>=13 ], cost: 1 15.69/10.31 15.69/10.31 6: f14 -> f10 : D'=1+D, [ 9>=E ], cost: 1 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 ### Simplification by acceleration and chaining ### 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 Eliminated locations (on tree-shaped paths): 15.69/10.31 15.69/10.31 Start location: f0 15.69/10.31 15.69/10.31 0: f0 -> f8 : A'=1, B'=1, C'=0, D'=1, E'=1, [], cost: 1 15.69/10.31 15.69/10.31 1: f8 -> f10 : [ 29>=D ], cost: 1 15.69/10.31 15.69/10.31 7: f10 -> f8 : D'=2+D, E'=-10+E, [ E>=D ], cost: 1 15.69/10.31 15.69/10.31 9: f10 -> f10 : D'=10+D, E'=free, [ D>=1+E && E>=6 && 12>=free && free>=10 ], cost: 2 15.69/10.31 15.69/10.31 10: f10 -> f10 : D'=1+D, E'=free, [ D>=1+E && E>=6 && free>=13 ], cost: 2 15.69/10.31 15.69/10.31 11: f10 -> f10 : D'=1+D, E'=free, [ D>=1+E && E>=6 && 9>=free ], cost: 2 15.69/10.31 15.69/10.31 12: f10 -> f10 : D'=1+D, E'=2+E, [ D>=1+E && 5>=E ], cost: 2 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 Accelerating simple loops of location 2. 15.69/10.31 15.69/10.31 Accelerating the following rules: 15.69/10.31 15.69/10.31 9: f10 -> f10 : D'=10+D, E'=free, [ D>=1+E && E>=6 && 12>=free && free>=10 ], cost: 2 15.69/10.31 15.69/10.31 10: f10 -> f10 : D'=1+D, E'=free, [ D>=1+E && E>=6 && free>=13 ], cost: 2 15.69/10.31 15.69/10.31 11: f10 -> f10 : D'=1+D, E'=free, [ D>=1+E && E>=6 && 9>=free ], cost: 2 15.69/10.31 15.69/10.31 12: f10 -> f10 : D'=1+D, E'=2+E, [ D>=1+E && 5>=E ], cost: 2 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 Accelerated rule 9 with NONTERM, yielding the new rule 13. 15.69/10.31 15.69/10.31 During metering: Instantiating temporary variables by {free==13} 15.69/10.31 15.69/10.31 Accelerated rule 10 with metering function meter (where 6*meter==D-E), yielding the new rule 14. 15.69/10.31 15.69/10.31 During metering: Instantiating temporary variables by {free==9} 15.69/10.31 15.69/10.31 Accelerated rule 11 with metering function meter_1 (where 2*meter_1==D-E), yielding the new rule 15. 15.69/10.31 15.69/10.31 Accelerated rule 12 with NONTERM (after adding D<=E), yielding the new rule 16. 15.69/10.31 15.69/10.31 Accelerated rule 12 with backward acceleration, yielding the new rule 17. 15.69/10.31 15.69/10.31 During metering: Instantiating temporary variables by {meter==14-D,free==9} 15.69/10.31 15.69/10.31 During metering: Instantiating temporary variables by {meter_1==10-D,free==13} 15.69/10.31 15.69/10.31 Nested simple loops 10 (outer loop) and 15 (inner loop) with NONTERM, resulting in the new rules: 18, 19. 15.69/10.31 15.69/10.31 During metering: Instantiating temporary variables by {k==1,free==13} 15.69/10.31 15.69/10.31 During metering: Instantiating temporary variables by {k==1,free==9} 15.69/10.31 15.69/10.31 During metering: Instantiating temporary variables by {k==1+D-free,free==5} 15.69/10.31 15.69/10.31 Nested simple loops 11 (outer loop) and 17 (inner loop) with metering function meter_4 (where 2*meter_4==-D+free), resulting in the new rules: 20. 15.69/10.31 15.69/10.31 Removing the simple loops: 9 10 11 12. 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 Accelerated all simple loops using metering functions (where possible): 15.69/10.31 15.69/10.31 Start location: f0 15.69/10.31 15.69/10.31 0: f0 -> f8 : A'=1, B'=1, C'=0, D'=1, E'=1, [], cost: 1 15.69/10.31 15.69/10.31 1: f8 -> f10 : [ 29>=D ], cost: 1 15.69/10.31 15.69/10.31 7: f10 -> f8 : D'=2+D, E'=-10+E, [ E>=D ], cost: 1 15.69/10.31 15.69/10.31 13: f10 -> [5] : [ D>=1+E && E>=6 && 12>=free && free>=10 ], cost: INF 15.69/10.31 15.69/10.31 14: f10 -> f10 : D'=D+meter, E'=13, [ D>=1+E && E>=6 && 6*meter==D-E && meter>=1 ], cost: 2*meter 15.69/10.31 15.69/10.31 15: f10 -> f10 : D'=meter_1+D, E'=9, [ D>=1+E && E>=6 && 2*meter_1==D-E && meter_1>=1 ], cost: 2*meter_1 15.69/10.31 15.69/10.31 16: f10 -> [5] : [ D>=1+E && 5>=E && D<=E ], cost: INF 15.69/10.31 15.69/10.31 17: f10 -> f10 : D'=k+D, E'=2*k+E, [ D>=1+E && 5>=E && k>0 && -1+k+D>=-1+2*k+E && 5>=-2+2*k+E ], cost: 2*k 15.69/10.31 15.69/10.31 18: f10 -> [5] : [ D>=1+E && E>=6 && 1-2*meter_1+D>=13 && 1+D>=2-2*meter_1+D && meter_1>=1 ], cost: INF 15.69/10.31 15.69/10.31 19: f10 -> [5] : D'=meter_1+D, E'=9, [ D>=1+E && E>=6 && 2*meter_1==D-E && meter_1>=1 && meter_1+D>=10 && 1-meter_1+D>=13 && 1+meter_1+D>=2-meter_1+D ], cost: INF 15.69/10.31 15.69/10.31 20: f10 -> f10 : D'=-2+2^(1+meter_4)+2^meter_4*D+free-2^meter_4*free, E'=3+2^meter_4*D+2*2^meter_4-2^meter_4*free, [ D>=1+E && E>=6 && 1+D>=6 && 1+D-free>0 && 1+2*D-free>=6+2*D-2*free && 5>=5+2*D-2*free && 2*meter_4==-D+free && meter_4>=1 ], cost: -4+2^(1+meter_4)*D+4*2^meter_4-2*D+2*free-2*2^meter_4*free 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 Chained accelerated rules (with incoming rules): 15.69/10.31 15.69/10.31 Start location: f0 15.69/10.31 15.69/10.31 0: f0 -> f8 : A'=1, B'=1, C'=0, D'=1, E'=1, [], cost: 1 15.69/10.31 15.69/10.31 1: f8 -> f10 : [ 29>=D ], cost: 1 15.69/10.31 15.69/10.31 21: f8 -> [5] : [ 29>=D && D>=1+E && E>=6 ], cost: INF 15.69/10.31 15.69/10.31 22: f8 -> f10 : D'=D+meter, E'=13, [ 29>=D && D>=1+E && E>=6 && 6*meter==D-E && meter>=1 ], cost: 1+2*meter 15.69/10.31 15.69/10.31 23: f8 -> f10 : D'=meter_1+D, E'=9, [ 29>=D && D>=1+E && E>=6 && 2*meter_1==D-E && meter_1>=1 ], cost: 1+2*meter_1 15.69/10.31 15.69/10.31 24: f8 -> f10 : D'=k+D, E'=2*k+E, [ 29>=D && D>=1+E && 5>=E && k>0 && -1+k+D>=-1+2*k+E && 5>=-2+2*k+E ], cost: 1+2*k 15.69/10.31 15.69/10.31 25: f8 -> [5] : [ 29>=D && D>=1+E && E>=6 && 1-2*meter_1+D>=13 && 1+D>=2-2*meter_1+D && meter_1>=1 ], cost: INF 15.69/10.31 15.69/10.31 26: f8 -> [5] : D'=meter_1+D, E'=9, [ 29>=D && D>=1+E && E>=6 && 2*meter_1==D-E && meter_1>=1 && meter_1+D>=10 && 1-meter_1+D>=13 && 1+meter_1+D>=2-meter_1+D ], cost: INF 15.69/10.31 15.69/10.31 7: f10 -> f8 : D'=2+D, E'=-10+E, [ E>=D ], cost: 1 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 Eliminated locations (on tree-shaped paths): 15.69/10.31 15.69/10.31 Start location: f0 15.69/10.31 15.69/10.31 0: f0 -> f8 : A'=1, B'=1, C'=0, D'=1, E'=1, [], cost: 1 15.69/10.31 15.69/10.31 21: f8 -> [5] : [ 29>=D && D>=1+E && E>=6 ], cost: INF 15.69/10.31 15.69/10.31 25: f8 -> [5] : [ 29>=D && D>=1+E && E>=6 && 1-2*meter_1+D>=13 && 1+D>=2-2*meter_1+D && meter_1>=1 ], cost: INF 15.69/10.31 15.69/10.31 26: f8 -> [5] : D'=meter_1+D, E'=9, [ 29>=D && D>=1+E && E>=6 && 2*meter_1==D-E && meter_1>=1 && meter_1+D>=10 && 1-meter_1+D>=13 && 1+meter_1+D>=2-meter_1+D ], cost: INF 15.69/10.31 15.69/10.31 27: f8 -> f8 : D'=2+D, E'=-10+E, [ 29>=D && E>=D ], cost: 2 15.69/10.31 15.69/10.31 28: f8 -> f8 : D'=2+D+meter, E'=3, [ 29>=D && D>=1+E && E>=6 && 6*meter==D-E && meter>=1 && 13>=D+meter ], cost: 2+2*meter 15.69/10.31 15.69/10.31 29: f8 -> f8 : D'=2+meter_1+D, E'=-1, [ 29>=D && D>=1+E && E>=6 && 2*meter_1==D-E && meter_1>=1 && 9>=meter_1+D ], cost: 2+2*meter_1 15.69/10.31 15.69/10.31 30: f8 -> f8 : D'=2+k+D, E'=-10+2*k+E, [ 29>=D && D>=1+E && 5>=E && k>0 && -1+k+D>=-1+2*k+E && 5>=-2+2*k+E && 2*k+E>=k+D ], cost: 2+2*k 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 Accelerating simple loops of location 1. 15.69/10.31 15.69/10.31 Simplified some of the simple loops (and removed duplicate rules). 15.69/10.31 15.69/10.31 Accelerating the following rules: 15.69/10.31 15.69/10.31 27: f8 -> f8 : D'=2+D, E'=-10+E, [ 29>=D && E>=D ], cost: 2 15.69/10.31 15.69/10.31 28: f8 -> f8 : D'=2+D+meter, E'=3, [ 29>=D && D>=1+E && E>=6 && 6*meter==D-E && meter>=1 && 13>=D+meter ], cost: 2+2*meter 15.69/10.31 15.69/10.31 29: f8 -> f8 : D'=2+meter_1+D, E'=-1, [ 29>=D && D>=1+E && E>=6 && 2*meter_1==D-E && meter_1>=1 && 9>=meter_1+D ], cost: 2+2*meter_1 15.69/10.31 15.69/10.31 30: f8 -> f8 : D'=2+2*D-E, E'=-10+2*D-E, [ 29>=D && D>=1+E && 5>=E && 5>=-2+2*D-E ], cost: 2+2*D-2*E 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 Accelerated rule 27 with metering function meter_5 (where 12*meter_5==-D+E) (after adding D>=E), yielding the new rule 31. 15.69/10.31 15.69/10.31 Accelerated rule 27 with backward acceleration, yielding the new rule 32. 15.69/10.31 15.69/10.31 Accelerated rule 28 with metering function meter_6 (where 11*meter_6==7-D-meter+E), yielding the new rule 33. 15.69/10.31 15.69/10.31 Accelerated rule 29 with metering function meter_7 (where 11*meter_7==3-meter_1-D+E), yielding the new rule 34. 15.69/10.31 15.69/10.31 Found no metering function for rule 30 (rule is too complicated). 15.69/10.31 15.69/10.31 Nested simple loops 28 (outer loop) and 32 (inner loop) with metering function 1-meter, resulting in the new rules: 35. 15.69/10.31 15.69/10.31 Nested simple loops 29 (outer loop) and 32 (inner loop) with metering function 1-meter_1, resulting in the new rules: 36. 15.69/10.31 15.69/10.31 Removing the simple loops: 27 28 29. 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 Accelerated all simple loops using metering functions (where possible): 15.69/10.31 15.69/10.31 Start location: f0 15.69/10.31 15.69/10.31 0: f0 -> f8 : A'=1, B'=1, C'=0, D'=1, E'=1, [], cost: 1 15.69/10.31 15.69/10.31 21: f8 -> [5] : [ 29>=D && D>=1+E && E>=6 ], cost: INF 15.69/10.31 15.69/10.31 25: f8 -> [5] : [ 29>=D && D>=1+E && E>=6 && 1-2*meter_1+D>=13 && 1+D>=2-2*meter_1+D && meter_1>=1 ], cost: INF 15.69/10.31 15.69/10.31 26: f8 -> [5] : D'=meter_1+D, E'=9, [ 29>=D && D>=1+E && E>=6 && 2*meter_1==D-E && meter_1>=1 && meter_1+D>=10 && 1-meter_1+D>=13 && 1+meter_1+D>=2-meter_1+D ], cost: INF 15.69/10.31 15.69/10.31 30: f8 -> f8 : D'=2+2*D-E, E'=-10+2*D-E, [ 29>=D && D>=1+E && 5>=E && 5>=-2+2*D-E ], cost: 2+2*D-2*E 15.69/10.31 15.69/10.31 31: f8 -> f8 : D'=D+2*meter_5, E'=-10*meter_5+E, [ 29>=D && E>=D && D>=E && 12*meter_5==-D+E && meter_5>=1 ], cost: 2*meter_5 15.69/10.31 15.69/10.31 32: f8 -> f8 : D'=2*k_1+D, E'=-10*k_1+E, [ 29>=D && E>=D && k_1>0 && 29>=-2+2*k_1+D && 10-10*k_1+E>=-2+2*k_1+D ], cost: 2*k_1 15.69/10.31 15.69/10.31 33: f8 -> f8 : D'=meter_6*meter+2*meter_6+D, E'=3, [ 29>=D && D>=1+E && E>=6 && 6*meter==D-E && meter>=1 && 13>=D+meter && 11*meter_6==7-D-meter+E && meter_6>=1 ], cost: 2*meter_6*meter+2*meter_6 15.69/10.31 15.69/10.31 34: f8 -> f8 : D'=meter_1*meter_7+D+2*meter_7, E'=-1, [ 29>=D && D>=1+E && E>=6 && 2*meter_1==D-E && meter_1>=1 && 9>=meter_1+D && 11*meter_7==3-meter_1-D+E && meter_7>=1 ], cost: 2*meter_1*meter_7+2*meter_7 15.69/10.31 15.69/10.31 35: f8 -> f8 : D'=2+D-2*meter-2*(-1+meter)*k_1-(-1+meter)*meter, E'=3, [ 29>=D && E>=D && k_1>0 && 10-10*k_1+E>=-2+2*k_1+D && 29>=2*k_1+D && 2*k_1+D>=1-10*k_1+E && -10*k_1+E>=6 && 6*meter==12*k_1+D-E && meter>=1 && 13>=2*k_1+D+meter && 1-meter>=1 ], cost: 2-2*meter-2*(-1+meter)*k_1-2*(-1+meter)*meter 15.69/10.31 15.69/10.31 36: f8 -> f8 : D'=2-2*k_1*(-1+meter_1)-meter_1*(-1+meter_1)-2*meter_1+D, E'=-1, [ 29>=D && E>=D && k_1>0 && 10-10*k_1+E>=-2+2*k_1+D && 29>=2*k_1+D && 2*k_1+D>=1-10*k_1+E && -10*k_1+E>=6 && 2*meter_1==12*k_1+D-E && meter_1>=1 && 9>=meter_1+2*k_1+D && 1-meter_1>=1 ], cost: 2-2*k_1*(-1+meter_1)-2*meter_1*(-1+meter_1)-2*meter_1 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 Chained accelerated rules (with incoming rules): 15.69/10.31 15.69/10.31 Start location: f0 15.69/10.31 15.69/10.31 0: f0 -> f8 : A'=1, B'=1, C'=0, D'=1, E'=1, [], cost: 1 15.69/10.31 15.69/10.31 37: f0 -> f8 : A'=1, B'=1, C'=0, D'=1+2*k_1, E'=1-10*k_1, [ k_1>0 && 29>=-1+2*k_1 && 11-10*k_1>=-1+2*k_1 ], cost: 1+2*k_1 15.69/10.31 15.69/10.31 21: f8 -> [5] : [ 29>=D && D>=1+E && E>=6 ], cost: INF 15.69/10.31 15.69/10.31 25: f8 -> [5] : [ 29>=D && D>=1+E && E>=6 && 1-2*meter_1+D>=13 && 1+D>=2-2*meter_1+D && meter_1>=1 ], cost: INF 15.69/10.31 15.69/10.31 26: f8 -> [5] : D'=meter_1+D, E'=9, [ 29>=D && D>=1+E && E>=6 && 2*meter_1==D-E && meter_1>=1 && meter_1+D>=10 && 1-meter_1+D>=13 && 1+meter_1+D>=2-meter_1+D ], cost: INF 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 Eliminated locations (on tree-shaped paths): 15.69/10.31 15.69/10.31 Start location: f0 15.69/10.31 15.69/10.31 38: f0 -> [7] : [ k_1>0 && 29>=-1+2*k_1 && 11-10*k_1>=-1+2*k_1 ], cost: 1+2*k_1 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 Applied pruning (of leafs and parallel rules): 15.69/10.31 15.69/10.31 Start location: f0 15.69/10.31 15.69/10.31 38: f0 -> [7] : [ k_1>0 && 29>=-1+2*k_1 && 11-10*k_1>=-1+2*k_1 ], cost: 1+2*k_1 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 ### Computing asymptotic complexity ### 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 Fully simplified ITS problem 15.69/10.31 15.69/10.31 Start location: f0 15.69/10.31 15.69/10.31 38: f0 -> [7] : [ k_1>0 && 29>=-1+2*k_1 && 11-10*k_1>=-1+2*k_1 ], cost: 1+2*k_1 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 Computing asymptotic complexity for rule 38 15.69/10.31 15.69/10.31 Simplified the guard: 15.69/10.31 15.69/10.31 38: f0 -> [7] : [ k_1>0 && 11-10*k_1>=-1+2*k_1 ], cost: 1+2*k_1 15.69/10.31 15.69/10.31 Could not solve the limit problem. 15.69/10.31 15.69/10.31 Resulting cost 0 has complexity: Unknown 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 Obtained the following overall complexity (w.r.t. the length of the input n): 15.69/10.31 15.69/10.31 Complexity: Unknown 15.69/10.31 15.69/10.31 Cpx degree: ? 15.69/10.31 15.69/10.31 Solved cost: 0 15.69/10.31 15.69/10.31 Rule cost: 0 15.69/10.31 15.69/10.31 Rule guard: [] 15.69/10.31 15.69/10.31 15.69/10.31 15.69/10.31 WORST_CASE(Omega(0),?) 15.69/10.31 15.69/10.31 15.69/10.31 ---------------------------------------- 15.69/10.31 15.69/10.31 (2) 15.69/10.31 BOUNDS(1, INF) 15.71/10.32 EOF