/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(NON_POLY, ?)
proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).

(0) CpxIntTrs
(1) Loat Proof [FINISHED, 2454 ms]
(2) BOUNDS(INF, INF)


----------------------------------------

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
evalfstart(A, B, C, D, E, F, G) -> Com_1(evalfentryin(A, B, C, D, E, F, G)) :|: TRUE
evalfentryin(A, B, C, D, E, F, G) -> Com_1(evalfbb10in(B, C, D, A, E, F, G)) :|: TRUE
evalfbb10in(A, B, C, D, E, F, G) -> Com_1(evalfbb8in(A, B, C, D, 1, F, G)) :|: D >= 1
evalfbb10in(A, B, C, D, E, F, G) -> Com_1(evalfreturnin(A, B, C, D, E, F, G)) :|: 0 >= D
evalfbb8in(A, B, C, D, E, F, G) -> Com_1(evalfbb6in(A, B, C, D, E, D, G)) :|: A >= E
evalfbb8in(A, B, C, D, E, F, G) -> Com_1(evalfbb9in(A, B, C, D, E, F, G)) :|: E >= A + 1
evalfbb6in(A, B, C, D, E, F, G) -> Com_1(evalfbb4in(A, B, C, D, E, F, C)) :|: B >= F
evalfbb6in(A, B, C, D, E, F, G) -> Com_1(evalfbb7in(A, B, C, D, E, F, G)) :|: F >= B + 1
evalfbb4in(A, B, C, D, E, F, G) -> Com_1(evalfbb3in(A, B, C, D, E, F, G)) :|: E >= G
evalfbb4in(A, B, C, D, E, F, G) -> Com_1(evalfbb5in(A, B, C, D, E, F, G)) :|: G >= E + 1
evalfbb3in(A, B, C, D, E, F, G) -> Com_1(evalfbb4in(A, B, C, D, E, F, G - 1)) :|: TRUE
evalfbb5in(A, B, C, D, E, F, G) -> Com_1(evalfbb6in(A, B, C, D, E, F + 1, G)) :|: TRUE
evalfbb7in(A, B, C, D, E, F, G) -> Com_1(evalfbb8in(A, B, C, D, E + 1, F, G)) :|: TRUE
evalfbb9in(A, B, C, D, E, F, G) -> Com_1(evalfbb10in(A, B, C, D - 1, E, F, G)) :|: TRUE
evalfreturnin(A, B, C, D, E, F, G) -> Com_1(evalfstop(A, B, C, D, E, F, G)) :|: TRUE

The start-symbols are:[evalfstart_7]


----------------------------------------

(1) Loat Proof (FINISHED)


### Pre-processing the ITS problem ###



Initial linear ITS problem

   Start location: evalfstart

      0: evalfstart -> evalfentryin : [], cost: 1

      1: evalfentryin -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 1

      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1

      3: evalfbb10in -> evalfreturnin : [ 0>=D ], cost: 1

      4: evalfbb8in -> evalfbb6in : F'=D, [ A>=E ], cost: 1

      5: evalfbb8in -> evalfbb9in : [ E>=1+A ], cost: 1

      6: evalfbb6in -> evalfbb4in : G'=C, [ B>=F ], cost: 1

      7: evalfbb6in -> evalfbb7in : [ F>=1+B ], cost: 1

      8: evalfbb4in -> evalfbb3in : [ E>=G ], cost: 1

      9: evalfbb4in -> evalfbb5in : [ G>=1+E ], cost: 1

     10: evalfbb3in -> evalfbb4in : G'=-1+G, [], cost: 1

     11: evalfbb5in -> evalfbb6in : F'=1+F, [], cost: 1

     12: evalfbb7in -> evalfbb8in : E'=1+E, [], cost: 1

     13: evalfbb9in -> evalfbb10in : D'=-1+D, [], cost: 1

     14: evalfreturnin -> evalfstop : [], cost: 1



Removed unreachable and leaf rules:

   Start location: evalfstart

      0: evalfstart -> evalfentryin : [], cost: 1

      1: evalfentryin -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 1

      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1

      4: evalfbb8in -> evalfbb6in : F'=D, [ A>=E ], cost: 1

      5: evalfbb8in -> evalfbb9in : [ E>=1+A ], cost: 1

      6: evalfbb6in -> evalfbb4in : G'=C, [ B>=F ], cost: 1

      7: evalfbb6in -> evalfbb7in : [ F>=1+B ], cost: 1

      8: evalfbb4in -> evalfbb3in : [ E>=G ], cost: 1

      9: evalfbb4in -> evalfbb5in : [ G>=1+E ], cost: 1

     10: evalfbb3in -> evalfbb4in : G'=-1+G, [], cost: 1

     11: evalfbb5in -> evalfbb6in : F'=1+F, [], cost: 1

     12: evalfbb7in -> evalfbb8in : E'=1+E, [], cost: 1

     13: evalfbb9in -> evalfbb10in : D'=-1+D, [], cost: 1



### Simplification by acceleration and chaining ###



Eliminated locations (on linear paths):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1

      4: evalfbb8in -> evalfbb6in : F'=D, [ A>=E ], cost: 1

     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2

      6: evalfbb6in -> evalfbb4in : G'=C, [ B>=F ], cost: 1

     17: evalfbb6in -> evalfbb8in : E'=1+E, [ F>=1+B ], cost: 2

     18: evalfbb4in -> evalfbb4in : G'=-1+G, [ E>=G ], cost: 2

     19: evalfbb4in -> evalfbb6in : F'=1+F, [ G>=1+E ], cost: 2



Accelerating simple loops of location 5.

   Accelerating the following rules:

     18: evalfbb4in -> evalfbb4in : G'=-1+G, [ E>=G ], cost: 2



   Accelerated rule 18 with NONTERM, yielding the new rule 20.

   Removing the simple loops: 18.



Accelerated all simple loops using metering functions (where possible):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1

      4: evalfbb8in -> evalfbb6in : F'=D, [ A>=E ], cost: 1

     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2

      6: evalfbb6in -> evalfbb4in : G'=C, [ B>=F ], cost: 1

     17: evalfbb6in -> evalfbb8in : E'=1+E, [ F>=1+B ], cost: 2

     19: evalfbb4in -> evalfbb6in : F'=1+F, [ G>=1+E ], cost: 2

     20: evalfbb4in -> [12] : [ E>=G ], cost: INF



Chained accelerated rules (with incoming rules):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1

      4: evalfbb8in -> evalfbb6in : F'=D, [ A>=E ], cost: 1

     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2

      6: evalfbb6in -> evalfbb4in : G'=C, [ B>=F ], cost: 1

     17: evalfbb6in -> evalfbb8in : E'=1+E, [ F>=1+B ], cost: 2

     21: evalfbb6in -> [12] : G'=C, [ B>=F && E>=C ], cost: INF

     19: evalfbb4in -> evalfbb6in : F'=1+F, [ G>=1+E ], cost: 2



Eliminated locations (on linear paths):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1

      4: evalfbb8in -> evalfbb6in : F'=D, [ A>=E ], cost: 1

     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2

     17: evalfbb6in -> evalfbb8in : E'=1+E, [ F>=1+B ], cost: 2

     21: evalfbb6in -> [12] : G'=C, [ B>=F && E>=C ], cost: INF

     22: evalfbb6in -> evalfbb6in : F'=1+F, G'=C, [ B>=F && C>=1+E ], cost: 3



Accelerating simple loops of location 4.

   Accelerating the following rules:

     22: evalfbb6in -> evalfbb6in : F'=1+F, G'=C, [ B>=F && C>=1+E ], cost: 3



   Accelerated rule 22 with metering function 1-F+B, yielding the new rule 23.

   Removing the simple loops: 22.



Accelerated all simple loops using metering functions (where possible):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1

      4: evalfbb8in -> evalfbb6in : F'=D, [ A>=E ], cost: 1

     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2

     17: evalfbb6in -> evalfbb8in : E'=1+E, [ F>=1+B ], cost: 2

     21: evalfbb6in -> [12] : G'=C, [ B>=F && E>=C ], cost: INF

     23: evalfbb6in -> evalfbb6in : F'=1+B, G'=C, [ B>=F && C>=1+E ], cost: 3-3*F+3*B



Chained accelerated rules (with incoming rules):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1

      4: evalfbb8in -> evalfbb6in : F'=D, [ A>=E ], cost: 1

     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2

     24: evalfbb8in -> evalfbb6in : F'=1+B, G'=C, [ A>=E && B>=D && C>=1+E ], cost: 4-3*D+3*B

     17: evalfbb6in -> evalfbb8in : E'=1+E, [ F>=1+B ], cost: 2

     21: evalfbb6in -> [12] : G'=C, [ B>=F && E>=C ], cost: INF



Eliminated locations (on tree-shaped paths):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1

     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2

     25: evalfbb8in -> evalfbb8in : E'=1+E, F'=D, [ A>=E && D>=1+B ], cost: 3

     26: evalfbb8in -> [12] : F'=D, G'=C, [ A>=E && B>=D && E>=C ], cost: INF

     27: evalfbb8in -> evalfbb8in : E'=1+E, F'=1+B, G'=C, [ A>=E && B>=D && C>=1+E ], cost: 6-3*D+3*B

     28: evalfbb8in -> [14] : [ A>=E && B>=D && C>=1+E ], cost: 4-3*D+3*B



Accelerating simple loops of location 3.

   Accelerating the following rules:

     25: evalfbb8in -> evalfbb8in : E'=1+E, F'=D, [ A>=E && D>=1+B ], cost: 3

     27: evalfbb8in -> evalfbb8in : E'=1+E, F'=1+B, G'=C, [ A>=E && B>=D && C>=1+E ], cost: 6-3*D+3*B



   Accelerated rule 25 with metering function 1+A-E, yielding the new rule 29.

   Accelerated rule 27 with backward acceleration, yielding the new rule 30.

   Accelerated rule 27 with backward acceleration, yielding the new rule 31.

   Removing the simple loops: 25 27.



Accelerated all simple loops using metering functions (where possible):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1

     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2

     26: evalfbb8in -> [12] : F'=D, G'=C, [ A>=E && B>=D && E>=C ], cost: INF

     28: evalfbb8in -> [14] : [ A>=E && B>=D && C>=1+E ], cost: 4-3*D+3*B

     29: evalfbb8in -> evalfbb8in : E'=1+A, F'=D, [ A>=E && D>=1+B ], cost: 3+3*A-3*E

     30: evalfbb8in -> evalfbb8in : E'=1+A, F'=1+B, G'=C, [ A>=E && B>=D && C>=1+E && C>=1+A ], cost: 6+3*(1+A-E)*B-3*D*(1+A-E)+6*A-6*E

     31: evalfbb8in -> evalfbb8in : E'=C, F'=1+B, G'=C, [ A>=E && B>=D && C>=1+E && A>=-1+C ], cost: 3*(C-E)*B+6*C-3*(C-E)*D-6*E



Chained accelerated rules (with incoming rules):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1

     32: evalfbb10in -> evalfbb8in : E'=1+A, F'=D, [ D>=1 && A>=1 && D>=1+B ], cost: 1+3*A

     33: evalfbb10in -> evalfbb8in : E'=1+A, F'=1+B, G'=C, [ D>=1 && A>=1 && B>=D && C>=2 && C>=1+A ], cost: 1+6*A-3*D*A+3*A*B

     34: evalfbb10in -> evalfbb8in : E'=C, F'=1+B, G'=C, [ D>=1 && A>=1 && B>=D && C>=2 && A>=-1+C ], cost: -5-3*D*(-1+C)+6*C+3*(-1+C)*B

     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2

     26: evalfbb8in -> [12] : F'=D, G'=C, [ A>=E && B>=D && E>=C ], cost: INF

     28: evalfbb8in -> [14] : [ A>=E && B>=D && C>=1+E ], cost: 4-3*D+3*B



Eliminated locations (on tree-shaped paths):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2

     35: evalfbb10in -> evalfbb10in : D'=-1+D, E'=1, [ D>=1 && 1>=1+A ], cost: 3

     36: evalfbb10in -> [12] : E'=1, F'=D, G'=C, [ D>=1 && A>=1 && B>=D && 1>=C ], cost: INF

     37: evalfbb10in -> [14] : E'=1, [ D>=1 && A>=1 && B>=D && C>=2 ], cost: 5-3*D+3*B

     38: evalfbb10in -> evalfbb10in : D'=-1+D, E'=1+A, F'=D, [ D>=1 && A>=1 && D>=1+B ], cost: 3+3*A

     39: evalfbb10in -> evalfbb10in : D'=-1+D, E'=1+A, F'=1+B, G'=C, [ D>=1 && A>=1 && B>=D && C>=2 && C>=1+A ], cost: 3+6*A-3*D*A+3*A*B

     40: evalfbb10in -> evalfbb10in : D'=-1+D, E'=C, F'=1+B, G'=C, [ D>=1 && A>=1 && B>=D && C>=2 && A>=-1+C && C>=1+A ], cost: -3-3*D*(-1+C)+6*C+3*(-1+C)*B

     41: evalfbb10in -> [12] : E'=C, F'=D, G'=C, [ D>=1 && A>=1 && B>=D && C>=2 && A>=C ], cost: INF

     42: evalfbb10in -> [16] : [ D>=1 && A>=1 && D>=1+B ], cost: 1+3*A

     43: evalfbb10in -> [16] : [ D>=1 && A>=1 && B>=D && C>=2 && C>=1+A ], cost: 1+6*A-3*D*A+3*A*B

     44: evalfbb10in -> [16] : [ D>=1 && A>=1 && B>=D && C>=2 && A>=-1+C ], cost: -5-3*D*(-1+C)+6*C+3*(-1+C)*B



Accelerating simple loops of location 2.

   Simplified some of the simple loops (and removed duplicate rules).

   Accelerating the following rules:

     35: evalfbb10in -> evalfbb10in : D'=-1+D, E'=1, [ D>=1 && 1>=1+A ], cost: 3

     38: evalfbb10in -> evalfbb10in : D'=-1+D, E'=1+A, F'=D, [ D>=1 && A>=1 && D>=1+B ], cost: 3+3*A

     39: evalfbb10in -> evalfbb10in : D'=-1+D, E'=1+A, F'=1+B, G'=C, [ D>=1 && A>=1 && B>=D && C>=2 && C>=1+A ], cost: 3+6*A-3*D*A+3*A*B

     40: evalfbb10in -> evalfbb10in : D'=-1+D, E'=C, F'=1+B, G'=C, [ D>=1 && A>=1 && B>=D && C>=2 && -1+C-A==0 ], cost: -3-3*D*(-1+C)+6*C+3*(-1+C)*B



   Accelerated rule 35 with metering function D, yielding the new rule 45.

   Accelerated rule 38 with backward acceleration, yielding the new rule 46.

   Accelerated rule 38 with backward acceleration, yielding the new rule 47.

   Accelerated rule 39 with metering function D, yielding the new rule 48.

   Accelerated rule 40 with metering function D, yielding the new rule 49.

   Removing the simple loops: 35 38 39 40.



Accelerated all simple loops using metering functions (where possible):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2

     36: evalfbb10in -> [12] : E'=1, F'=D, G'=C, [ D>=1 && A>=1 && B>=D && 1>=C ], cost: INF

     37: evalfbb10in -> [14] : E'=1, [ D>=1 && A>=1 && B>=D && C>=2 ], cost: 5-3*D+3*B

     41: evalfbb10in -> [12] : E'=C, F'=D, G'=C, [ D>=1 && A>=1 && B>=D && C>=2 && A>=C ], cost: INF

     42: evalfbb10in -> [16] : [ D>=1 && A>=1 && D>=1+B ], cost: 1+3*A

     43: evalfbb10in -> [16] : [ D>=1 && A>=1 && B>=D && C>=2 && C>=1+A ], cost: 1+6*A-3*D*A+3*A*B

     44: evalfbb10in -> [16] : [ D>=1 && A>=1 && B>=D && C>=2 && A>=-1+C ], cost: -5-3*D*(-1+C)+6*C+3*(-1+C)*B

     45: evalfbb10in -> evalfbb10in : D'=0, E'=1, [ D>=1 && 1>=1+A ], cost: 3*D

     46: evalfbb10in -> evalfbb10in : D'=0, E'=1+A, F'=1, [ D>=1 && A>=1 && D>=1+B && 1>=1+B ], cost: 3*D+3*D*A

     47: evalfbb10in -> evalfbb10in : D'=B, E'=1+A, F'=1+B, [ D>=1 && A>=1 && D>=1+B && 1+B>=1 ], cost: 3*(D-B)*A+3*D-3*B

     48: evalfbb10in -> evalfbb10in : D'=0, E'=1+A, F'=1+B, G'=C, [ D>=1 && A>=1 && B>=D && C>=2 && C>=1+A ], cost: -3/2*D^2*A+3*D+3*D*A*B+9/2*D*A

     49: evalfbb10in -> evalfbb10in : D'=0, E'=C, F'=1+B, G'=C, [ D>=1 && A>=1 && B>=D && C>=2 && -1+C-A==0 ], cost: -3*D*B+9/2*C*D-3/2*D+3/2*D^2-3/2*C*D^2+3*C*D*B



Chained accelerated rules (with incoming rules):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2

     50: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=0, E'=1, [ A>=1 && 1>=1+B ], cost: 2+3*A

     51: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=0, E'=1+B, F'=1, [ A>=1 && B>=1 && A>=1+C && 1>=1+C ], cost: 2+3*A+3*A*B

     52: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=C, E'=1+B, F'=1+C, [ A>=1 && B>=1 && A>=1+C && 1+C>=1 ], cost: 2-3*(C-A)*B-3*C+3*A

     53: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=0, E'=1+B, F'=1+C, G'=D, [ A>=1 && B>=1 && C>=A && D>=2 && D>=1+B ], cost: 2+3*C*A*B-3/2*A^2*B+3*A+9/2*A*B

     54: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=0, E'=D, F'=1+C, G'=D, [ A>=1 && B>=1 && C>=A && D>=2 && -1+D-B==0 ], cost: 2+3*C*D*A-3/2*A+9/2*D*A-3/2*D*A^2+3/2*A^2-3*C*A

     36: evalfbb10in -> [12] : E'=1, F'=D, G'=C, [ D>=1 && A>=1 && B>=D && 1>=C ], cost: INF

     37: evalfbb10in -> [14] : E'=1, [ D>=1 && A>=1 && B>=D && C>=2 ], cost: 5-3*D+3*B

     41: evalfbb10in -> [12] : E'=C, F'=D, G'=C, [ D>=1 && A>=1 && B>=D && C>=2 && A>=C ], cost: INF

     42: evalfbb10in -> [16] : [ D>=1 && A>=1 && D>=1+B ], cost: 1+3*A

     43: evalfbb10in -> [16] : [ D>=1 && A>=1 && B>=D && C>=2 && C>=1+A ], cost: 1+6*A-3*D*A+3*A*B

     44: evalfbb10in -> [16] : [ D>=1 && A>=1 && B>=D && C>=2 && A>=-1+C ], cost: -5-3*D*(-1+C)+6*C+3*(-1+C)*B



Eliminated locations (on tree-shaped paths):

   Start location: evalfstart

     55: evalfstart -> [12] : A'=B, B'=C, C'=D, D'=A, E'=1, F'=A, G'=D, [ A>=1 && B>=1 && C>=A && 1>=D ], cost: INF

     56: evalfstart -> [14] : A'=B, B'=C, C'=D, D'=A, E'=1, [ A>=1 && B>=1 && C>=A && D>=2 ], cost: 7+3*C-3*A

     57: evalfstart -> [12] : A'=B, B'=C, C'=D, D'=A, E'=D, F'=A, G'=D, [ A>=1 && B>=1 && C>=A && D>=2 && B>=D ], cost: INF

     58: evalfstart -> [16] : A'=B, B'=C, C'=D, D'=A, [ A>=1 && B>=1 && A>=1+C ], cost: 3+3*B

     59: evalfstart -> [16] : A'=B, B'=C, C'=D, D'=A, [ A>=1 && B>=1 && C>=A && D>=2 && D>=1+B ], cost: 3+3*C*B-3*A*B+6*B

     60: evalfstart -> [16] : A'=B, B'=C, C'=D, D'=A, [ A>=1 && B>=1 && C>=A && D>=2 && B>=-1+D ], cost: -3+3*C*(-1+D)+6*D-3*(-1+D)*A

     61: evalfstart -> [12] : A'=B, B'=C, C'=D, D'=C, E'=1, F'=C, G'=D, [ A>=1 && B>=1 && A>=1+C && C>=1 && 1>=D ], cost: INF

     62: evalfstart -> [14] : A'=B, B'=C, C'=D, D'=C, E'=1, F'=1+C, [ A>=1 && B>=1 && A>=1+C && C>=1 && D>=2 ], cost: 7-3*(C-A)*B-3*C+3*A

     63: evalfstart -> [12] : A'=B, B'=C, C'=D, D'=C, E'=D, F'=C, G'=D, [ A>=1 && B>=1 && A>=1+C && C>=1 && D>=2 && B>=D ], cost: INF

     64: evalfstart -> [16] : A'=B, B'=C, C'=D, D'=C, E'=1+B, F'=1+C, [ A>=1 && B>=1 && A>=1+C && C>=1 && D>=2 && D>=1+B ], cost: 3-3*(C-A)*B-3*C+3*A+6*B

     65: evalfstart -> [16] : A'=B, B'=C, C'=D, D'=C, E'=1+B, F'=1+C, [ A>=1 && B>=1 && A>=1+C && C>=1 && D>=2 && B>=-1+D ], cost: -3-3*(C-A)*B-3*C+6*D+3*A

     66: evalfstart -> [18] : [ A>=1 && 1>=1+B ], cost: 2+3*A

     67: evalfstart -> [18] : [ A>=1 && B>=1 && A>=1+C && 1>=1+C ], cost: 2+3*A+3*A*B

     68: evalfstart -> [18] : [ A>=1 && B>=1 && A>=1+C && 1+C>=1 ], cost: 2-3*(C-A)*B-3*C+3*A

     69: evalfstart -> [18] : [ A>=1 && B>=1 && C>=A && D>=2 && D>=1+B ], cost: 2+3*C*A*B-3/2*A^2*B+3*A+9/2*A*B

     70: evalfstart -> [18] : [ A>=1 && B>=1 && C>=A && D>=2 && -1+D-B==0 ], cost: 2+3*C*D*A-3/2*A+9/2*D*A-3/2*D*A^2+3/2*A^2-3*C*A



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: evalfstart

     55: evalfstart -> [12] : A'=B, B'=C, C'=D, D'=A, E'=1, F'=A, G'=D, [ A>=1 && B>=1 && C>=A && 1>=D ], cost: INF

     56: evalfstart -> [14] : A'=B, B'=C, C'=D, D'=A, E'=1, [ A>=1 && B>=1 && C>=A && D>=2 ], cost: 7+3*C-3*A

     57: evalfstart -> [12] : A'=B, B'=C, C'=D, D'=A, E'=D, F'=A, G'=D, [ A>=1 && B>=1 && C>=A && D>=2 && B>=D ], cost: INF

     58: evalfstart -> [16] : A'=B, B'=C, C'=D, D'=A, [ A>=1 && B>=1 && A>=1+C ], cost: 3+3*B

     59: evalfstart -> [16] : A'=B, B'=C, C'=D, D'=A, [ A>=1 && B>=1 && C>=A && D>=2 && D>=1+B ], cost: 3+3*C*B-3*A*B+6*B

     60: evalfstart -> [16] : A'=B, B'=C, C'=D, D'=A, [ A>=1 && B>=1 && C>=A && D>=2 && B>=-1+D ], cost: -3+3*C*(-1+D)+6*D-3*(-1+D)*A

     61: evalfstart -> [12] : A'=B, B'=C, C'=D, D'=C, E'=1, F'=C, G'=D, [ A>=1 && B>=1 && A>=1+C && C>=1 && 1>=D ], cost: INF

     62: evalfstart -> [14] : A'=B, B'=C, C'=D, D'=C, E'=1, F'=1+C, [ A>=1 && B>=1 && A>=1+C && C>=1 && D>=2 ], cost: 7-3*(C-A)*B-3*C+3*A

     63: evalfstart -> [12] : A'=B, B'=C, C'=D, D'=C, E'=D, F'=C, G'=D, [ A>=1 && B>=1 && A>=1+C && C>=1 && D>=2 && B>=D ], cost: INF

     64: evalfstart -> [16] : A'=B, B'=C, C'=D, D'=C, E'=1+B, F'=1+C, [ A>=1 && B>=1 && A>=1+C && C>=1 && D>=2 && D>=1+B ], cost: 3-3*(C-A)*B-3*C+3*A+6*B

     65: evalfstart -> [16] : A'=B, B'=C, C'=D, D'=C, E'=1+B, F'=1+C, [ A>=1 && B>=1 && A>=1+C && C>=1 && D>=2 && B>=-1+D ], cost: -3-3*(C-A)*B-3*C+6*D+3*A

     66: evalfstart -> [18] : [ A>=1 && 1>=1+B ], cost: 2+3*A

     67: evalfstart -> [18] : [ A>=1 && B>=1 && A>=1+C && 1>=1+C ], cost: 2+3*A+3*A*B

     68: evalfstart -> [18] : [ A>=1 && B>=1 && A>=1+C && 1+C>=1 ], cost: 2-3*(C-A)*B-3*C+3*A

     69: evalfstart -> [18] : [ A>=1 && B>=1 && C>=A && D>=2 && D>=1+B ], cost: 2+3*C*A*B-3/2*A^2*B+3*A+9/2*A*B

     70: evalfstart -> [18] : [ A>=1 && B>=1 && C>=A && D>=2 && -1+D-B==0 ], cost: 2+3*C*D*A-3/2*A+9/2*D*A-3/2*D*A^2+3/2*A^2-3*C*A



Computing asymptotic complexity for rule 55

   Resulting cost INF has complexity: Nonterm



Found new complexity Nonterm.



Obtained the following overall complexity (w.r.t. the length of the input n):

   Complexity:  Nonterm

   Cpx degree:  Nonterm

   Solved cost: INF

   Rule cost:   INF

   Rule guard:  [ A>=1 && B>=1 && C>=A && 1>=D ]



NO


----------------------------------------

(2)
BOUNDS(INF, INF)