11.22/4.26	WORST_CASE(NON_POLY, ?)
11.46/4.27	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
11.46/4.27	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.46/4.27	
11.46/4.27	
11.46/4.27	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
11.46/4.27	
11.46/4.27	(0) CpxIntTrs
11.46/4.27	(1) Loat Proof [FINISHED, 2544 ms]
11.46/4.27	(2) BOUNDS(INF, INF)
11.46/4.27	
11.46/4.27	
11.46/4.27	----------------------------------------
11.46/4.27	
11.46/4.27	(0)
11.46/4.27	Obligation:
11.46/4.27	Complexity Int TRS consisting of the following rules:
11.46/4.27	evalfstart(A, B, C, D, E, F, G) -> Com_1(evalfentryin(A, B, C, D, E, F, G)) :|: TRUE
11.46/4.27	evalfentryin(A, B, C, D, E, F, G) -> Com_1(evalfbb10in(B, C, D, A, E, F, G)) :|: TRUE
11.46/4.27	evalfbb10in(A, B, C, D, E, F, G) -> Com_1(evalfbb8in(A, B, C, D, 1, F, G)) :|: D >= 1
11.46/4.27	evalfbb10in(A, B, C, D, E, F, G) -> Com_1(evalfreturnin(A, B, C, D, E, F, G)) :|: 0 >= D
11.46/4.27	evalfbb8in(A, B, C, D, E, F, G) -> Com_1(evalfbb6in(A, B, C, D, E, D, G)) :|: A >= E
11.46/4.27	evalfbb8in(A, B, C, D, E, F, G) -> Com_1(evalfbb9in(A, B, C, D, E, F, G)) :|: E >= A + 1
11.46/4.27	evalfbb6in(A, B, C, D, E, F, G) -> Com_1(evalfbb4in(A, B, C, D, E, F, C)) :|: B >= F
11.46/4.27	evalfbb6in(A, B, C, D, E, F, G) -> Com_1(evalfbb7in(A, B, C, D, E, F, G)) :|: F >= B + 1
11.46/4.27	evalfbb4in(A, B, C, D, E, F, G) -> Com_1(evalfbb3in(A, B, C, D, E, F, G)) :|: E >= G
11.46/4.27	evalfbb4in(A, B, C, D, E, F, G) -> Com_1(evalfbb5in(A, B, C, D, E, F, G)) :|: G >= E + 1
11.46/4.27	evalfbb3in(A, B, C, D, E, F, G) -> Com_1(evalfbb4in(A, B, C, D, E, F, G - 1)) :|: TRUE
11.46/4.27	evalfbb5in(A, B, C, D, E, F, G) -> Com_1(evalfbb6in(A, B, C, D, E, F + 1, G)) :|: TRUE
11.46/4.27	evalfbb7in(A, B, C, D, E, F, G) -> Com_1(evalfbb8in(A, B, C, D, E + 1, F, G)) :|: TRUE
11.46/4.27	evalfbb9in(A, B, C, D, E, F, G) -> Com_1(evalfbb10in(A, B, C, D - 1, E, F, G)) :|: TRUE
11.46/4.27	evalfreturnin(A, B, C, D, E, F, G) -> Com_1(evalfstop(A, B, C, D, E, F, G)) :|: TRUE
11.46/4.27	
11.46/4.27	The start-symbols are:[evalfstart_7]
11.46/4.27	
11.46/4.27	
11.46/4.27	----------------------------------------
11.46/4.27	
11.46/4.27	(1) Loat Proof (FINISHED)
11.46/4.27	
11.46/4.27	
11.46/4.27	### Pre-processing the ITS problem ###
11.46/4.27	
11.46/4.27	
11.46/4.27	
11.46/4.27	Initial linear ITS problem
11.46/4.27	
11.46/4.27	   Start location: evalfstart
11.46/4.27	
11.46/4.27	      0: evalfstart -> evalfentryin : [], cost: 1
11.46/4.27	
11.46/4.27	      1: evalfentryin -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 1
11.46/4.27	
11.46/4.27	      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1
11.46/4.27	
11.46/4.27	      3: evalfbb10in -> evalfreturnin : [ 0>=D ], cost: 1
11.46/4.27	
11.46/4.27	      4: evalfbb8in -> evalfbb6in : F'=D, [ A>=E ], cost: 1
11.46/4.27	
11.46/4.27	      5: evalfbb8in -> evalfbb9in : [ E>=1+A ], cost: 1
11.46/4.27	
11.46/4.27	      6: evalfbb6in -> evalfbb4in : G'=C, [ B>=F ], cost: 1
11.46/4.27	
11.46/4.27	      7: evalfbb6in -> evalfbb7in : [ F>=1+B ], cost: 1
11.46/4.27	
11.46/4.27	      8: evalfbb4in -> evalfbb3in : [ E>=G ], cost: 1
11.46/4.27	
11.46/4.27	      9: evalfbb4in -> evalfbb5in : [ G>=1+E ], cost: 1
11.46/4.27	
11.46/4.27	     10: evalfbb3in -> evalfbb4in : G'=-1+G, [], cost: 1
11.46/4.27	
11.46/4.27	     11: evalfbb5in -> evalfbb6in : F'=1+F, [], cost: 1
11.46/4.27	
11.46/4.27	     12: evalfbb7in -> evalfbb8in : E'=1+E, [], cost: 1
11.46/4.27	
11.46/4.27	     13: evalfbb9in -> evalfbb10in : D'=-1+D, [], cost: 1
11.46/4.27	
11.46/4.27	     14: evalfreturnin -> evalfstop : [], cost: 1
11.46/4.27	
11.46/4.27	
11.46/4.27	
11.46/4.27	Removed unreachable and leaf rules:
11.46/4.27	
11.46/4.27	   Start location: evalfstart
11.46/4.27	
11.46/4.27	      0: evalfstart -> evalfentryin : [], cost: 1
11.46/4.27	
11.46/4.27	      1: evalfentryin -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 1
11.46/4.27	
11.46/4.27	      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1
11.46/4.27	
11.46/4.27	      4: evalfbb8in -> evalfbb6in : F'=D, [ A>=E ], cost: 1
11.46/4.27	
11.46/4.27	      5: evalfbb8in -> evalfbb9in : [ E>=1+A ], cost: 1
11.46/4.27	
11.46/4.27	      6: evalfbb6in -> evalfbb4in : G'=C, [ B>=F ], cost: 1
11.46/4.27	
11.46/4.27	      7: evalfbb6in -> evalfbb7in : [ F>=1+B ], cost: 1
11.46/4.27	
11.46/4.27	      8: evalfbb4in -> evalfbb3in : [ E>=G ], cost: 1
11.46/4.27	
11.46/4.27	      9: evalfbb4in -> evalfbb5in : [ G>=1+E ], cost: 1
11.46/4.27	
11.46/4.27	     10: evalfbb3in -> evalfbb4in : G'=-1+G, [], cost: 1
11.46/4.27	
11.46/4.27	     11: evalfbb5in -> evalfbb6in : F'=1+F, [], cost: 1
11.46/4.27	
11.46/4.27	     12: evalfbb7in -> evalfbb8in : E'=1+E, [], cost: 1
11.46/4.27	
11.46/4.27	     13: evalfbb9in -> evalfbb10in : D'=-1+D, [], cost: 1
11.46/4.27	
11.46/4.27	
11.46/4.27	
11.46/4.27	### Simplification by acceleration and chaining ###
11.46/4.27	
11.46/4.27	
11.46/4.27	
11.46/4.27	Eliminated locations (on linear paths):
11.46/4.27	
11.46/4.27	   Start location: evalfstart
11.46/4.27	
11.46/4.27	     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2
11.46/4.27	
11.46/4.27	      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1
11.46/4.27	
11.46/4.27	      4: evalfbb8in -> evalfbb6in : F'=D, [ A>=E ], cost: 1
11.46/4.27	
11.46/4.27	     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2
11.46/4.27	
11.46/4.27	      6: evalfbb6in -> evalfbb4in : G'=C, [ B>=F ], cost: 1
11.46/4.27	
11.46/4.27	     17: evalfbb6in -> evalfbb8in : E'=1+E, [ F>=1+B ], cost: 2
11.46/4.27	
11.46/4.27	     18: evalfbb4in -> evalfbb4in : G'=-1+G, [ E>=G ], cost: 2
11.46/4.27	
11.46/4.27	     19: evalfbb4in -> evalfbb6in : F'=1+F, [ G>=1+E ], cost: 2
11.46/4.27	
11.46/4.27	
11.46/4.27	
11.46/4.27	Accelerating simple loops of location 5.
11.46/4.27	
11.46/4.27	   Accelerating the following rules:
11.46/4.27	
11.46/4.27	     18: evalfbb4in -> evalfbb4in : G'=-1+G, [ E>=G ], cost: 2
11.46/4.27	
11.46/4.27	
11.46/4.27	
11.46/4.27	   Accelerated rule 18 with NONTERM, yielding the new rule 20.
11.46/4.27	
11.46/4.27	   Removing the simple loops: 18.
11.46/4.27	
11.46/4.27	
11.46/4.27	
11.46/4.27	Accelerated all simple loops using metering functions (where possible):
11.46/4.27	
11.46/4.27	   Start location: evalfstart
11.46/4.27	
11.46/4.27	     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2
11.46/4.27	
11.46/4.27	      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1
11.46/4.27	
11.46/4.27	      4: evalfbb8in -> evalfbb6in : F'=D, [ A>=E ], cost: 1
11.46/4.27	
11.46/4.27	     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2
11.46/4.27	
11.46/4.27	      6: evalfbb6in -> evalfbb4in : G'=C, [ B>=F ], cost: 1
11.46/4.27	
11.46/4.27	     17: evalfbb6in -> evalfbb8in : E'=1+E, [ F>=1+B ], cost: 2
11.46/4.27	
11.46/4.27	     19: evalfbb4in -> evalfbb6in : F'=1+F, [ G>=1+E ], cost: 2
11.46/4.27	
11.46/4.27	     20: evalfbb4in -> [12] : [ E>=G ], cost: INF
11.46/4.27	
11.46/4.27	
11.46/4.27	
11.46/4.27	Chained accelerated rules (with incoming rules):
11.46/4.27	
11.46/4.27	   Start location: evalfstart
11.46/4.27	
11.46/4.27	     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2
11.46/4.27	
11.46/4.27	      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1
11.46/4.27	
11.46/4.27	      4: evalfbb8in -> evalfbb6in : F'=D, [ A>=E ], cost: 1
11.46/4.27	
11.46/4.27	     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2
11.46/4.27	
11.46/4.27	      6: evalfbb6in -> evalfbb4in : G'=C, [ B>=F ], cost: 1
11.46/4.27	
11.46/4.27	     17: evalfbb6in -> evalfbb8in : E'=1+E, [ F>=1+B ], cost: 2
11.46/4.27	
11.46/4.27	     21: evalfbb6in -> [12] : G'=C, [ B>=F && E>=C ], cost: INF
11.46/4.27	
11.46/4.27	     19: evalfbb4in -> evalfbb6in : F'=1+F, [ G>=1+E ], cost: 2
11.46/4.27	
11.46/4.27	
11.46/4.27	
11.46/4.27	Eliminated locations (on linear paths):
11.46/4.27	
11.46/4.27	   Start location: evalfstart
11.46/4.27	
11.46/4.27	     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2
11.46/4.27	
11.46/4.27	      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1
11.46/4.27	
11.46/4.27	      4: evalfbb8in -> evalfbb6in : F'=D, [ A>=E ], cost: 1
11.46/4.27	
11.46/4.27	     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2
11.46/4.27	
11.46/4.27	     17: evalfbb6in -> evalfbb8in : E'=1+E, [ F>=1+B ], cost: 2
11.46/4.27	
11.46/4.27	     21: evalfbb6in -> [12] : G'=C, [ B>=F && E>=C ], cost: INF
11.46/4.27	
11.46/4.27	     22: evalfbb6in -> evalfbb6in : F'=1+F, G'=C, [ B>=F && C>=1+E ], cost: 3
11.46/4.27	
11.46/4.27	
11.46/4.27	
11.46/4.27	Accelerating simple loops of location 4.
11.46/4.27	
11.46/4.27	   Accelerating the following rules:
11.46/4.27	
11.46/4.27	     22: evalfbb6in -> evalfbb6in : F'=1+F, G'=C, [ B>=F && C>=1+E ], cost: 3
11.46/4.27	
11.46/4.27	
11.46/4.27	
11.46/4.27	   Accelerated rule 22 with metering function 1-F+B, yielding the new rule 23.
11.46/4.27	
11.46/4.27	   Removing the simple loops: 22.
11.46/4.27	
11.46/4.27	
11.46/4.27	
11.46/4.27	Accelerated all simple loops using metering functions (where possible):
11.46/4.27	
11.46/4.27	   Start location: evalfstart
11.46/4.27	
11.46/4.27	     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2
11.46/4.27	
11.46/4.27	      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1
11.46/4.27	
11.46/4.27	      4: evalfbb8in -> evalfbb6in : F'=D, [ A>=E ], cost: 1
11.46/4.27	
11.46/4.27	     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2
11.46/4.27	
11.46/4.27	     17: evalfbb6in -> evalfbb8in : E'=1+E, [ F>=1+B ], cost: 2
11.46/4.27	
11.46/4.27	     21: evalfbb6in -> [12] : G'=C, [ B>=F && E>=C ], cost: INF
11.46/4.27	
11.46/4.27	     23: evalfbb6in -> evalfbb6in : F'=1+B, G'=C, [ B>=F && C>=1+E ], cost: 3-3*F+3*B
11.46/4.27	
11.46/4.27	
11.46/4.27	
11.46/4.27	Chained accelerated rules (with incoming rules):
11.46/4.27	
11.46/4.27	   Start location: evalfstart
11.46/4.27	
11.46/4.27	     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2
11.46/4.27	
11.46/4.27	      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1
11.46/4.27	
11.46/4.27	      4: evalfbb8in -> evalfbb6in : F'=D, [ A>=E ], cost: 1
11.46/4.27	
11.46/4.27	     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2
11.46/4.27	
11.46/4.27	     24: evalfbb8in -> evalfbb6in : F'=1+B, G'=C, [ A>=E && B>=D && C>=1+E ], cost: 4-3*D+3*B
11.46/4.27	
11.46/4.27	     17: evalfbb6in -> evalfbb8in : E'=1+E, [ F>=1+B ], cost: 2
11.46/4.27	
11.46/4.27	     21: evalfbb6in -> [12] : G'=C, [ B>=F && E>=C ], cost: INF
11.46/4.27	
11.46/4.27	
11.46/4.27	
11.46/4.27	Eliminated locations (on tree-shaped paths):
11.46/4.27	
11.46/4.27	   Start location: evalfstart
11.46/4.27	
11.46/4.27	     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2
11.46/4.27	
11.46/4.27	      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1
11.46/4.27	
11.46/4.27	     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2
11.46/4.27	
11.46/4.27	     25: evalfbb8in -> evalfbb8in : E'=1+E, F'=D, [ A>=E && D>=1+B ], cost: 3
11.46/4.27	
11.46/4.27	     26: evalfbb8in -> [12] : F'=D, G'=C, [ A>=E && B>=D && E>=C ], cost: INF
11.51/4.27	
11.51/4.27	     27: evalfbb8in -> evalfbb8in : E'=1+E, F'=1+B, G'=C, [ A>=E && B>=D && C>=1+E ], cost: 6-3*D+3*B
11.51/4.27	
11.51/4.27	     28: evalfbb8in -> [14] : [ A>=E && B>=D && C>=1+E ], cost: 4-3*D+3*B
11.51/4.27	
11.51/4.27	
11.51/4.27	
11.51/4.27	Accelerating simple loops of location 3.
11.51/4.27	
11.51/4.27	   Accelerating the following rules:
11.51/4.27	
11.51/4.27	     25: evalfbb8in -> evalfbb8in : E'=1+E, F'=D, [ A>=E && D>=1+B ], cost: 3
11.51/4.27	
11.51/4.27	     27: evalfbb8in -> evalfbb8in : E'=1+E, F'=1+B, G'=C, [ A>=E && B>=D && C>=1+E ], cost: 6-3*D+3*B
11.51/4.27	
11.51/4.27	
11.51/4.27	
11.51/4.27	   Accelerated rule 25 with metering function 1+A-E, yielding the new rule 29.
11.51/4.27	
11.51/4.27	   Accelerated rule 27 with backward acceleration, yielding the new rule 30.
11.51/4.27	
11.51/4.27	   Accelerated rule 27 with backward acceleration, yielding the new rule 31.
11.51/4.27	
11.51/4.27	   Removing the simple loops: 25 27.
11.51/4.27	
11.51/4.27	
11.51/4.27	
11.51/4.27	Accelerated all simple loops using metering functions (where possible):
11.51/4.27	
11.51/4.27	   Start location: evalfstart
11.51/4.27	
11.51/4.27	     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2
11.51/4.27	
11.51/4.27	      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1
11.51/4.27	
11.51/4.27	     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2
11.51/4.27	
11.51/4.27	     26: evalfbb8in -> [12] : F'=D, G'=C, [ A>=E && B>=D && E>=C ], cost: INF
11.51/4.27	
11.51/4.27	     28: evalfbb8in -> [14] : [ A>=E && B>=D && C>=1+E ], cost: 4-3*D+3*B
11.51/4.27	
11.51/4.27	     29: evalfbb8in -> evalfbb8in : E'=1+A, F'=D, [ A>=E && D>=1+B ], cost: 3+3*A-3*E
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	
11.51/4.27	
11.51/4.27	Chained accelerated rules (with incoming rules):
11.51/4.27	
11.51/4.27	   Start location: evalfstart
11.51/4.27	
11.51/4.27	     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2
11.51/4.27	
11.51/4.27	      2: evalfbb10in -> evalfbb8in : E'=1, [ D>=1 ], cost: 1
11.51/4.27	
11.51/4.27	     32: evalfbb10in -> evalfbb8in : E'=1+A, F'=D, [ D>=1 && A>=1 && D>=1+B ], cost: 1+3*A
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     16: evalfbb8in -> evalfbb10in : D'=-1+D, [ E>=1+A ], cost: 2
11.51/4.27	
11.51/4.27	     26: evalfbb8in -> [12] : F'=D, G'=C, [ A>=E && B>=D && E>=C ], cost: INF
11.51/4.27	
11.51/4.27	     28: evalfbb8in -> [14] : [ A>=E && B>=D && C>=1+E ], cost: 4-3*D+3*B
11.51/4.27	
11.51/4.27	
11.51/4.27	
11.51/4.27	Eliminated locations (on tree-shaped paths):
11.51/4.27	
11.51/4.27	   Start location: evalfstart
11.51/4.27	
11.51/4.27	     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2
11.51/4.27	
11.51/4.27	     35: evalfbb10in -> evalfbb10in : D'=-1+D, E'=1, [ D>=1 && 1>=1+A ], cost: 3
11.51/4.27	
11.51/4.27	     36: evalfbb10in -> [12] : E'=1, F'=D, G'=C, [ D>=1 && A>=1 && B>=D && 1>=C ], cost: INF
11.51/4.27	
11.51/4.27	     37: evalfbb10in -> [14] : E'=1, [ D>=1 && A>=1 && B>=D && C>=2 ], cost: 5-3*D+3*B
11.51/4.27	
11.51/4.27	     38: evalfbb10in -> evalfbb10in : D'=-1+D, E'=1+A, F'=D, [ D>=1 && A>=1 && D>=1+B ], cost: 3+3*A
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     41: evalfbb10in -> [12] : E'=C, F'=D, G'=C, [ D>=1 && A>=1 && B>=D && C>=2 && A>=C ], cost: INF
11.51/4.27	
11.51/4.27	     42: evalfbb10in -> [16] : [ D>=1 && A>=1 && D>=1+B ], cost: 1+3*A
11.51/4.27	
11.51/4.27	     43: evalfbb10in -> [16] : [ D>=1 && A>=1 && B>=D && C>=2 && C>=1+A ], cost: 1+6*A-3*D*A+3*A*B
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	
11.51/4.27	
11.51/4.27	Accelerating simple loops of location 2.
11.51/4.27	
11.51/4.27	   Simplified some of the simple loops (and removed duplicate rules).
11.51/4.27	
11.51/4.27	   Accelerating the following rules:
11.51/4.27	
11.51/4.27	     35: evalfbb10in -> evalfbb10in : D'=-1+D, E'=1, [ D>=1 && 1>=1+A ], cost: 3
11.51/4.27	
11.51/4.27	     38: evalfbb10in -> evalfbb10in : D'=-1+D, E'=1+A, F'=D, [ D>=1 && A>=1 && D>=1+B ], cost: 3+3*A
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	
11.51/4.27	
11.51/4.27	   Accelerated rule 35 with metering function D, yielding the new rule 45.
11.51/4.27	
11.51/4.27	   Accelerated rule 38 with backward acceleration, yielding the new rule 46.
11.51/4.27	
11.51/4.27	   Accelerated rule 38 with backward acceleration, yielding the new rule 47.
11.51/4.27	
11.51/4.27	   Accelerated rule 39 with metering function D, yielding the new rule 48.
11.51/4.27	
11.51/4.27	   Accelerated rule 40 with metering function D, yielding the new rule 49.
11.51/4.27	
11.51/4.27	   Removing the simple loops: 35 38 39 40.
11.51/4.27	
11.51/4.27	
11.51/4.27	
11.51/4.27	Accelerated all simple loops using metering functions (where possible):
11.51/4.27	
11.51/4.27	   Start location: evalfstart
11.51/4.27	
11.51/4.27	     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2
11.51/4.27	
11.51/4.27	     36: evalfbb10in -> [12] : E'=1, F'=D, G'=C, [ D>=1 && A>=1 && B>=D && 1>=C ], cost: INF
11.51/4.27	
11.51/4.27	     37: evalfbb10in -> [14] : E'=1, [ D>=1 && A>=1 && B>=D && C>=2 ], cost: 5-3*D+3*B
11.51/4.27	
11.51/4.27	     41: evalfbb10in -> [12] : E'=C, F'=D, G'=C, [ D>=1 && A>=1 && B>=D && C>=2 && A>=C ], cost: INF
11.51/4.27	
11.51/4.27	     42: evalfbb10in -> [16] : [ D>=1 && A>=1 && D>=1+B ], cost: 1+3*A
11.51/4.27	
11.51/4.27	     43: evalfbb10in -> [16] : [ D>=1 && A>=1 && B>=D && C>=2 && C>=1+A ], cost: 1+6*A-3*D*A+3*A*B
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     45: evalfbb10in -> evalfbb10in : D'=0, E'=1, [ D>=1 && 1>=1+A ], cost: 3*D
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	
11.51/4.27	
11.51/4.27	Chained accelerated rules (with incoming rules):
11.51/4.27	
11.51/4.27	   Start location: evalfstart
11.51/4.27	
11.51/4.27	     15: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=A, [], cost: 2
11.51/4.27	
11.51/4.27	     50: evalfstart -> evalfbb10in : A'=B, B'=C, C'=D, D'=0, E'=1, [ A>=1 && 1>=1+B ], cost: 2+3*A
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     36: evalfbb10in -> [12] : E'=1, F'=D, G'=C, [ D>=1 && A>=1 && B>=D && 1>=C ], cost: INF
11.51/4.27	
11.51/4.27	     37: evalfbb10in -> [14] : E'=1, [ D>=1 && A>=1 && B>=D && C>=2 ], cost: 5-3*D+3*B
11.51/4.27	
11.51/4.27	     41: evalfbb10in -> [12] : E'=C, F'=D, G'=C, [ D>=1 && A>=1 && B>=D && C>=2 && A>=C ], cost: INF
11.51/4.27	
11.51/4.27	     42: evalfbb10in -> [16] : [ D>=1 && A>=1 && D>=1+B ], cost: 1+3*A
11.51/4.27	
11.51/4.27	     43: evalfbb10in -> [16] : [ D>=1 && A>=1 && B>=D && C>=2 && C>=1+A ], cost: 1+6*A-3*D*A+3*A*B
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	
11.51/4.27	
11.51/4.27	Eliminated locations (on tree-shaped paths):
11.51/4.27	
11.51/4.27	   Start location: evalfstart
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     58: evalfstart -> [16] : A'=B, B'=C, C'=D, D'=A, [ A>=1 && B>=1 && A>=1+C ], cost: 3+3*B
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     66: evalfstart -> [18] : [ A>=1 && 1>=1+B ], cost: 2+3*A
11.51/4.27	
11.51/4.27	     67: evalfstart -> [18] : [ A>=1 && B>=1 && A>=1+C && 1>=1+C ], cost: 2+3*A+3*A*B
11.51/4.27	
11.51/4.27	     68: evalfstart -> [18] : [ A>=1 && B>=1 && A>=1+C && 1+C>=1 ], cost: 2-3*(C-A)*B-3*C+3*A
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	
11.51/4.27	
11.51/4.27	### Computing asymptotic complexity ###
11.51/4.27	
11.51/4.27	
11.51/4.27	
11.51/4.27	Fully simplified ITS problem
11.51/4.27	
11.51/4.27	   Start location: evalfstart
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     58: evalfstart -> [16] : A'=B, B'=C, C'=D, D'=A, [ A>=1 && B>=1 && A>=1+C ], cost: 3+3*B
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     66: evalfstart -> [18] : [ A>=1 && 1>=1+B ], cost: 2+3*A
11.51/4.27	
11.51/4.27	     67: evalfstart -> [18] : [ A>=1 && B>=1 && A>=1+C && 1>=1+C ], cost: 2+3*A+3*A*B
11.51/4.27	
11.51/4.27	     68: evalfstart -> [18] : [ A>=1 && B>=1 && A>=1+C && 1+C>=1 ], cost: 2-3*(C-A)*B-3*C+3*A
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	     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
11.51/4.27	
11.51/4.27	
11.51/4.27	
11.51/4.27	Computing asymptotic complexity for rule 55
11.51/4.27	
11.51/4.27	   Resulting cost INF has complexity: Nonterm
11.51/4.27	
11.51/4.27	
11.51/4.27	
11.51/4.27	Found new complexity Nonterm.
11.51/4.27	
11.51/4.27	
11.51/4.27	
11.51/4.27	Obtained the following overall complexity (w.r.t. the length of the input n):
11.51/4.27	
11.51/4.27	   Complexity:  Nonterm
11.51/4.27	
11.51/4.27	   Cpx degree:  Nonterm
11.51/4.27	
11.51/4.27	   Solved cost: INF
11.51/4.27	
11.51/4.27	   Rule cost:   INF
11.51/4.27	
11.51/4.27	   Rule guard:  [ A>=1 && B>=1 && C>=A && 1>=D ]
11.51/4.27	
11.51/4.27	
11.51/4.27	
11.51/4.27	NO
11.51/4.27	
11.51/4.27	
11.51/4.27	----------------------------------------
11.51/4.27	
11.51/4.27	(2)
11.51/4.27	BOUNDS(INF, INF)
11.53/4.31	EOF