15.10/5.52	WORST_CASE(NON_POLY, ?)
15.10/5.53	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
15.10/5.53	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
15.10/5.53	
15.10/5.53	
15.10/5.53	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
15.10/5.53	
15.10/5.53	(0) CpxIntTrs
15.10/5.53	(1) Loat Proof [FINISHED, 3815 ms]
15.10/5.53	(2) BOUNDS(INF, INF)
15.10/5.53	
15.10/5.53	
15.10/5.53	----------------------------------------
15.10/5.53	
15.10/5.53	(0)
15.10/5.53	Obligation:
15.10/5.53	Complexity Int TRS consisting of the following rules:
15.10/5.53	f0(A, B, C, D, E, F, G, H) -> Com_1(f15(10, 35, 285, I, I, 0, G, H)) :|: TRUE
15.10/5.53	f15(A, B, C, D, E, F, G, H) -> Com_1(f25(A, B, C, D, E, F, I, 1)) :|: A >= F + 1
15.10/5.53	f25(A, B, C, D, E, F, G, H) -> Com_1(f25(A, B, C, D, E, F, I, H + 1)) :|: E >= H + 1
15.10/5.53	f41(A, B, C, D, E, F, G, H) -> Com_1(f15(A, B, C, D, E, F + 1, G, H)) :|: E >= B
15.10/5.53	f41(A, B, C, D, E, F, G, H) -> Com_1(f15(A, B, C, D, E + 1, F + 1, G, H)) :|: B >= E + 1
15.10/5.53	f25(A, B, C, D, E, F, G, H) -> Com_1(f41(A, B, C, D, E, F, G, H)) :|: H >= E && I >= J + 1
15.10/5.53	f25(A, B, C, D, E, F, G, H) -> Com_1(f41(A, B, C, D, E, F, G, H)) :|: H >= E
15.10/5.53	f25(A, B, C, D, E, F, G, H) -> Com_1(f15(A, B, C, D, E - 1, F + 1, G, H)) :|: H >= E
15.10/5.53	f15(A, B, C, D, E, F, G, H) -> Com_1(f48(A, B, C, D, E, F, G, H)) :|: F >= A
15.10/5.53	
15.10/5.53	The start-symbols are:[f0_8]
15.10/5.53	
15.10/5.53	
15.10/5.53	----------------------------------------
15.10/5.53	
15.10/5.53	(1) Loat Proof (FINISHED)
15.10/5.53	
15.10/5.53	
15.10/5.53	### Pre-processing the ITS problem ###
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Initial linear ITS problem
15.10/5.53	
15.10/5.53	   Start location: f0
15.10/5.53	
15.10/5.53	      0: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=free, F'=0, [], cost: 1
15.10/5.53	
15.10/5.53	      1: f15 -> f25 : G'=free_1, H'=1, [ A>=1+F ], cost: 1
15.10/5.53	
15.10/5.53	      8: f15 -> f48 : [ F>=A ], cost: 1
15.10/5.53	
15.10/5.53	      2: f25 -> f25 : G'=free_2, H'=1+H, [ E>=1+H ], cost: 1
15.10/5.53	
15.10/5.53	      5: f25 -> f41 : [ H>=E && free_3>=1+free_4 ], cost: 1
15.10/5.53	
15.10/5.53	      6: f25 -> f41 : [ H>=E ], cost: 1
15.10/5.53	
15.10/5.53	      7: f25 -> f15 : E'=-1+E, F'=1+F, [ H>=E ], cost: 1
15.10/5.53	
15.10/5.53	      3: f41 -> f15 : F'=1+F, [ E>=B ], cost: 1
15.10/5.53	
15.10/5.53	      4: f41 -> f15 : E'=1+E, F'=1+F, [ B>=1+E ], cost: 1
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Removed unreachable and leaf rules:
15.10/5.53	
15.10/5.53	   Start location: f0
15.10/5.53	
15.10/5.53	      0: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=free, F'=0, [], cost: 1
15.10/5.53	
15.10/5.53	      1: f15 -> f25 : G'=free_1, H'=1, [ A>=1+F ], cost: 1
15.10/5.53	
15.10/5.53	      2: f25 -> f25 : G'=free_2, H'=1+H, [ E>=1+H ], cost: 1
15.10/5.53	
15.10/5.53	      5: f25 -> f41 : [ H>=E && free_3>=1+free_4 ], cost: 1
15.10/5.53	
15.10/5.53	      6: f25 -> f41 : [ H>=E ], cost: 1
15.10/5.53	
15.10/5.53	      7: f25 -> f15 : E'=-1+E, F'=1+F, [ H>=E ], cost: 1
15.10/5.53	
15.10/5.53	      3: f41 -> f15 : F'=1+F, [ E>=B ], cost: 1
15.10/5.53	
15.10/5.53	      4: f41 -> f15 : E'=1+E, F'=1+F, [ B>=1+E ], cost: 1
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Simplified all rules, resulting in:
15.10/5.53	
15.10/5.53	   Start location: f0
15.10/5.53	
15.10/5.53	      0: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=free, F'=0, [], cost: 1
15.10/5.53	
15.10/5.53	      1: f15 -> f25 : G'=free_1, H'=1, [ A>=1+F ], cost: 1
15.10/5.53	
15.10/5.53	      2: f25 -> f25 : G'=free_2, H'=1+H, [ E>=1+H ], cost: 1
15.10/5.53	
15.10/5.53	      6: f25 -> f41 : [ H>=E ], cost: 1
15.10/5.53	
15.10/5.53	      7: f25 -> f15 : E'=-1+E, F'=1+F, [ H>=E ], cost: 1
15.10/5.53	
15.10/5.53	      3: f41 -> f15 : F'=1+F, [ E>=B ], cost: 1
15.10/5.53	
15.10/5.53	      4: f41 -> f15 : E'=1+E, F'=1+F, [ B>=1+E ], cost: 1
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	### Simplification by acceleration and chaining ###
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Accelerating simple loops of location 2.
15.10/5.53	
15.10/5.53	   Accelerating the following rules:
15.10/5.53	
15.10/5.53	      2: f25 -> f25 : G'=free_2, H'=1+H, [ E>=1+H ], cost: 1
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	   Accelerated rule 2 with metering function -H+E, yielding the new rule 9.
15.10/5.53	
15.10/5.53	   Removing the simple loops: 2.
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Accelerated all simple loops using metering functions (where possible):
15.10/5.53	
15.10/5.53	   Start location: f0
15.10/5.53	
15.10/5.53	      0: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=free, F'=0, [], cost: 1
15.10/5.53	
15.10/5.53	      1: f15 -> f25 : G'=free_1, H'=1, [ A>=1+F ], cost: 1
15.10/5.53	
15.10/5.53	      6: f25 -> f41 : [ H>=E ], cost: 1
15.10/5.53	
15.10/5.53	      7: f25 -> f15 : E'=-1+E, F'=1+F, [ H>=E ], cost: 1
15.10/5.53	
15.10/5.53	      9: f25 -> f25 : G'=free_2, H'=E, [ E>=1+H ], cost: -H+E
15.10/5.53	
15.10/5.53	      3: f41 -> f15 : F'=1+F, [ E>=B ], cost: 1
15.10/5.53	
15.10/5.53	      4: f41 -> f15 : E'=1+E, F'=1+F, [ B>=1+E ], cost: 1
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Chained accelerated rules (with incoming rules):
15.10/5.53	
15.10/5.53	   Start location: f0
15.10/5.53	
15.10/5.53	      0: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=free, F'=0, [], cost: 1
15.10/5.53	
15.10/5.53	      1: f15 -> f25 : G'=free_1, H'=1, [ A>=1+F ], cost: 1
15.10/5.53	
15.10/5.53	     10: f15 -> f25 : G'=free_2, H'=E, [ A>=1+F && E>=2 ], cost: E
15.10/5.53	
15.10/5.53	      6: f25 -> f41 : [ H>=E ], cost: 1
15.10/5.53	
15.10/5.53	      7: f25 -> f15 : E'=-1+E, F'=1+F, [ H>=E ], cost: 1
15.10/5.53	
15.10/5.53	      3: f41 -> f15 : F'=1+F, [ E>=B ], cost: 1
15.10/5.53	
15.10/5.53	      4: f41 -> f15 : E'=1+E, F'=1+F, [ B>=1+E ], cost: 1
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Eliminated locations (on tree-shaped paths):
15.10/5.53	
15.10/5.53	   Start location: f0
15.10/5.53	
15.10/5.53	      0: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=free, F'=0, [], cost: 1
15.10/5.53	
15.10/5.53	     11: f15 -> f41 : G'=free_1, H'=1, [ A>=1+F && 1>=E ], cost: 2
15.10/5.53	
15.10/5.53	     12: f15 -> f15 : E'=-1+E, F'=1+F, G'=free_1, H'=1, [ A>=1+F && 1>=E ], cost: 2
15.10/5.53	
15.10/5.53	     13: f15 -> f41 : G'=free_2, H'=E, [ A>=1+F && E>=2 ], cost: 1+E
15.10/5.53	
15.10/5.53	     14: f15 -> f15 : E'=-1+E, F'=1+F, G'=free_2, H'=E, [ A>=1+F && E>=2 ], cost: 1+E
15.10/5.53	
15.10/5.53	      3: f41 -> f15 : F'=1+F, [ E>=B ], cost: 1
15.10/5.53	
15.10/5.53	      4: f41 -> f15 : E'=1+E, F'=1+F, [ B>=1+E ], cost: 1
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Accelerating simple loops of location 1.
15.10/5.53	
15.10/5.53	   Accelerating the following rules:
15.10/5.53	
15.10/5.53	     12: f15 -> f15 : E'=-1+E, F'=1+F, G'=free_1, H'=1, [ A>=1+F && 1>=E ], cost: 2
15.10/5.53	
15.10/5.53	     14: f15 -> f15 : E'=-1+E, F'=1+F, G'=free_2, H'=E, [ A>=1+F && E>=2 ], cost: 1+E
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	   Accelerated rule 12 with metering function -F+A, yielding the new rule 15.
15.10/5.53	
15.10/5.53	   Accelerated rule 14 with backward acceleration, yielding the new rule 16.
15.10/5.53	
15.10/5.53	   Accelerated rule 14 with backward acceleration, yielding the new rule 17.
15.10/5.53	
15.10/5.53	   Removing the simple loops: 12 14.
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Accelerated all simple loops using metering functions (where possible):
15.10/5.53	
15.10/5.53	   Start location: f0
15.10/5.53	
15.10/5.53	      0: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=free, F'=0, [], cost: 1
15.10/5.53	
15.10/5.53	     11: f15 -> f41 : G'=free_1, H'=1, [ A>=1+F && 1>=E ], cost: 2
15.10/5.53	
15.10/5.53	     13: f15 -> f41 : G'=free_2, H'=E, [ A>=1+F && E>=2 ], cost: 1+E
15.10/5.53	
15.10/5.53	     15: f15 -> f15 : E'=F-A+E, F'=A, G'=free_1, H'=1, [ A>=1+F && 1>=E ], cost: -2*F+2*A
15.10/5.53	
15.10/5.53	     16: f15 -> f15 : E'=F-A+E, F'=A, G'=free_2, H'=1+F-A+E, [ A>=1+F && E>=2 && 1+F-A+E>=2 ], cost: -3/2*F+3/2*A-1/2*(F-A)^2-(F-A)*E
15.10/5.53	
15.10/5.53	     17: f15 -> f15 : E'=1, F'=-1+F+E, G'=free_2, H'=2, [ A>=1+F && E>=2 && A>=-1+F+E ], cost: -3/2+(-1+E)*E+3/2*E-1/2*(-1+E)^2
15.10/5.53	
15.10/5.53	      3: f41 -> f15 : F'=1+F, [ E>=B ], cost: 1
15.10/5.53	
15.10/5.53	      4: f41 -> f15 : E'=1+E, F'=1+F, [ B>=1+E ], cost: 1
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Chained accelerated rules (with incoming rules):
15.10/5.53	
15.10/5.53	   Start location: f0
15.10/5.53	
15.10/5.53	      0: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=free, F'=0, [], cost: 1
15.10/5.53	
15.10/5.53	     18: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=-10+free, F'=10, G'=free_1, H'=1, [ 1>=free ], cost: 21
15.10/5.53	
15.10/5.53	     21: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=-10+free, F'=10, G'=free_2, H'=-9+free, [ -9+free>=2 ], cost: -34+10*free
15.10/5.53	
15.10/5.53	     24: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=1, F'=-1+free, G'=free_2, H'=2, [ free>=2 && 10>=-1+free ], cost: -1/2-1/2*(-1+free)^2+free*(-1+free)+3/2*free
15.10/5.53	
15.10/5.53	     11: f15 -> f41 : G'=free_1, H'=1, [ A>=1+F && 1>=E ], cost: 2
15.10/5.53	
15.10/5.53	     13: f15 -> f41 : G'=free_2, H'=E, [ A>=1+F && E>=2 ], cost: 1+E
15.10/5.53	
15.10/5.53	      3: f41 -> f15 : F'=1+F, [ E>=B ], cost: 1
15.10/5.53	
15.10/5.53	      4: f41 -> f15 : E'=1+E, F'=1+F, [ B>=1+E ], cost: 1
15.10/5.53	
15.10/5.53	     19: f41 -> f15 : E'=1+F-A+E, F'=A, G'=free_1, H'=1, [ E>=B && A>=2+F && 1>=E ], cost: -1-2*F+2*A
15.10/5.53	
15.10/5.53	     20: f41 -> f15 : E'=2+F-A+E, F'=A, G'=free_1, H'=1, [ B>=1+E && A>=2+F && 1>=1+E ], cost: -1-2*F+2*A
15.10/5.53	
15.10/5.53	     22: f41 -> f15 : E'=1+F-A+E, F'=A, G'=free_2, H'=2+F-A+E, [ E>=B && A>=2+F && E>=2 && 2+F-A+E>=2 ], cost: -1/2-3/2*F-(1+F-A)*E+3/2*A-1/2*(1+F-A)^2
15.10/5.53	
15.10/5.53	     23: f41 -> f15 : E'=2+F-A+E, F'=A, G'=free_2, H'=3+F-A+E, [ B>=1+E && A>=2+F && 1+E>=2 && 3+F-A+E>=2 ], cost: -1/2-3/2*F-(1+F-A)*(1+E)+3/2*A-1/2*(1+F-A)^2
15.10/5.53	
15.10/5.53	     25: f41 -> f15 : E'=1, F'=F+E, G'=free_2, H'=2, [ E>=B && A>=2+F && E>=2 && A>=F+E ], cost: -1/2+(-1+E)*E+3/2*E-1/2*(-1+E)^2
15.10/5.53	
15.10/5.53	     26: f41 -> f15 : E'=1, F'=1+F+E, G'=free_2, H'=2, [ B>=1+E && A>=2+F && 1+E>=2 && A>=1+F+E ], cost: 1-1/2*E^2+(1+E)*E+3/2*E
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Eliminated locations (on tree-shaped paths):
15.10/5.53	
15.10/5.53	   Start location: f0
15.10/5.53	
15.10/5.53	      0: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=free, F'=0, [], cost: 1
15.10/5.53	
15.10/5.53	     18: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=-10+free, F'=10, G'=free_1, H'=1, [ 1>=free ], cost: 21
15.10/5.53	
15.10/5.53	     21: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=-10+free, F'=10, G'=free_2, H'=-9+free, [ -9+free>=2 ], cost: -34+10*free
15.10/5.53	
15.10/5.53	     24: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=1, F'=-1+free, G'=free_2, H'=2, [ free>=2 && 10>=-1+free ], cost: -1/2-1/2*(-1+free)^2+free*(-1+free)+3/2*free
15.10/5.53	
15.10/5.53	     27: f15 -> f15 : F'=1+F, G'=free_1, H'=1, [ A>=1+F && 1>=E && E>=B ], cost: 3
15.10/5.53	
15.10/5.53	     28: f15 -> f15 : E'=1+E, F'=1+F, G'=free_1, H'=1, [ A>=1+F && 1>=E && B>=1+E ], cost: 3
15.10/5.53	
15.10/5.53	     29: f15 -> f15 : E'=1+F-A+E, F'=A, G'=free_1, H'=1, [ 1>=E && E>=B && A>=2+F ], cost: 1-2*F+2*A
15.10/5.53	
15.10/5.53	     30: f15 -> f15 : E'=2+F-A+E, F'=A, G'=free_1, H'=1, [ B>=1+E && A>=2+F && 1>=1+E ], cost: 1-2*F+2*A
15.10/5.53	
15.10/5.53	     31: f15 -> f15 : E'=2+F-A+E, F'=A, G'=free_2, H'=3+F-A+E, [ 1>=E && B>=1+E && A>=2+F && 1+E>=2 && 3+F-A+E>=2 ], cost: 3/2-3/2*F-(1+F-A)*(1+E)+3/2*A-1/2*(1+F-A)^2
15.10/5.53	
15.10/5.53	     32: f15 -> f15 : E'=1, F'=1+F+E, G'=free_2, H'=2, [ 1>=E && B>=1+E && A>=2+F && 1+E>=2 && A>=1+F+E ], cost: 3-1/2*E^2+(1+E)*E+3/2*E
15.10/5.53	
15.10/5.53	     33: f15 -> f15 : F'=1+F, G'=free_2, H'=E, [ A>=1+F && E>=2 && E>=B ], cost: 2+E
15.10/5.53	
15.10/5.53	     34: f15 -> f15 : E'=1+E, F'=1+F, G'=free_2, H'=E, [ A>=1+F && E>=2 && B>=1+E ], cost: 2+E
15.10/5.53	
15.10/5.53	     35: f15 -> f15 : E'=1+F-A+E, F'=A, G'=free_2, H'=2+F-A+E, [ E>=2 && E>=B && A>=2+F && 2+F-A+E>=2 ], cost: 1/2-3/2*F-(1+F-A)*E+3/2*A+E-1/2*(1+F-A)^2
15.10/5.53	
15.10/5.53	     36: f15 -> f15 : E'=2+F-A+E, F'=A, G'=free_2, H'=3+F-A+E, [ E>=2 && B>=1+E && A>=2+F && 3+F-A+E>=2 ], cost: 1/2-3/2*F-(1+F-A)*(1+E)+3/2*A+E-1/2*(1+F-A)^2
15.10/5.53	
15.10/5.53	     37: f15 -> f15 : E'=1, F'=F+E, G'=free_2, H'=2, [ E>=2 && E>=B && A>=2+F && A>=F+E ], cost: 1/2+(-1+E)*E+5/2*E-1/2*(-1+E)^2
15.10/5.53	
15.10/5.53	     38: f15 -> f15 : E'=1, F'=1+F+E, G'=free_2, H'=2, [ E>=2 && B>=1+E && A>=2+F && A>=1+F+E ], cost: 2-1/2*E^2+(1+E)*E+5/2*E
15.10/5.53	
15.10/5.53	     39: f15 -> [7] : [ A>=1+F && E>=2 ], cost: 1+E
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Applied pruning (of leafs and parallel rules):
15.10/5.53	
15.10/5.53	   Start location: f0
15.10/5.53	
15.10/5.53	      0: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=free, F'=0, [], cost: 1
15.10/5.53	
15.10/5.53	     18: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=-10+free, F'=10, G'=free_1, H'=1, [ 1>=free ], cost: 21
15.10/5.53	
15.10/5.53	     21: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=-10+free, F'=10, G'=free_2, H'=-9+free, [ -9+free>=2 ], cost: -34+10*free
15.10/5.53	
15.10/5.53	     24: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=1, F'=-1+free, G'=free_2, H'=2, [ free>=2 && 10>=-1+free ], cost: -1/2-1/2*(-1+free)^2+free*(-1+free)+3/2*free
15.10/5.53	
15.10/5.53	     33: f15 -> f15 : F'=1+F, G'=free_2, H'=E, [ A>=1+F && E>=2 && E>=B ], cost: 2+E
15.10/5.53	
15.10/5.53	     35: f15 -> f15 : E'=1+F-A+E, F'=A, G'=free_2, H'=2+F-A+E, [ E>=2 && E>=B && A>=2+F && 2+F-A+E>=2 ], cost: 1/2-3/2*F-(1+F-A)*E+3/2*A+E-1/2*(1+F-A)^2
15.10/5.53	
15.10/5.53	     36: f15 -> f15 : E'=2+F-A+E, F'=A, G'=free_2, H'=3+F-A+E, [ E>=2 && B>=1+E && A>=2+F && 3+F-A+E>=2 ], cost: 1/2-3/2*F-(1+F-A)*(1+E)+3/2*A+E-1/2*(1+F-A)^2
15.10/5.53	
15.10/5.53	     37: f15 -> f15 : E'=1, F'=F+E, G'=free_2, H'=2, [ E>=2 && E>=B && A>=2+F && A>=F+E ], cost: 1/2+(-1+E)*E+5/2*E-1/2*(-1+E)^2
15.10/5.53	
15.10/5.53	     38: f15 -> f15 : E'=1, F'=1+F+E, G'=free_2, H'=2, [ E>=2 && B>=1+E && A>=2+F && A>=1+F+E ], cost: 2-1/2*E^2+(1+E)*E+5/2*E
15.10/5.53	
15.10/5.53	     39: f15 -> [7] : [ A>=1+F && E>=2 ], cost: 1+E
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Accelerating simple loops of location 1.
15.10/5.53	
15.10/5.53	   Accelerating the following rules:
15.10/5.53	
15.10/5.53	     33: f15 -> f15 : F'=1+F, G'=free_2, H'=E, [ A>=1+F && E>=2 && E>=B ], cost: 2+E
15.10/5.53	
15.10/5.53	     35: f15 -> f15 : E'=1+F-A+E, F'=A, G'=free_2, H'=2+F-A+E, [ E>=2 && E>=B && A>=2+F && 2+F-A+E>=2 ], cost: 1/2-3/2*F-(1+F-A)*E+3/2*A+E-1/2*(1+F-A)^2
15.10/5.53	
15.10/5.53	     36: f15 -> f15 : E'=2+F-A+E, F'=A, G'=free_2, H'=3+F-A+E, [ E>=2 && B>=1+E && A>=2+F && 3+F-A+E>=2 ], cost: 1/2-3/2*F-(1+F-A)*(1+E)+3/2*A+E-1/2*(1+F-A)^2
15.10/5.53	
15.10/5.53	     37: f15 -> f15 : E'=1, F'=F+E, G'=free_2, H'=2, [ E>=2 && E>=B && A>=2+F && A>=F+E ], cost: 1/2+(-1+E)*E+5/2*E-1/2*(-1+E)^2
15.10/5.53	
15.10/5.53	     38: f15 -> f15 : E'=1, F'=1+F+E, G'=free_2, H'=2, [ E>=2 && B>=1+E && A>=2+F && A>=1+F+E ], cost: 2-1/2*E^2+(1+E)*E+5/2*E
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	   Accelerated rule 33 with metering function -F+A, yielding the new rule 40.
15.10/5.53	
15.10/5.53	   Found no metering function for rule 35.
15.10/5.53	
15.10/5.53	   Found no metering function for rule 36.
15.10/5.53	
15.10/5.53	   Found no metering function for rule 37.
15.10/5.53	
15.10/5.53	   Found no metering function for rule 38.
15.10/5.53	
15.10/5.53	   Removing the simple loops: 33.
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Accelerated all simple loops using metering functions (where possible):
15.10/5.53	
15.10/5.53	   Start location: f0
15.10/5.53	
15.10/5.53	      0: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=free, F'=0, [], cost: 1
15.10/5.53	
15.10/5.53	     18: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=-10+free, F'=10, G'=free_1, H'=1, [ 1>=free ], cost: 21
15.10/5.53	
15.10/5.53	     21: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=-10+free, F'=10, G'=free_2, H'=-9+free, [ -9+free>=2 ], cost: -34+10*free
15.10/5.53	
15.10/5.53	     24: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=1, F'=-1+free, G'=free_2, H'=2, [ free>=2 && 10>=-1+free ], cost: -1/2-1/2*(-1+free)^2+free*(-1+free)+3/2*free
15.10/5.53	
15.10/5.53	     35: f15 -> f15 : E'=1+F-A+E, F'=A, G'=free_2, H'=2+F-A+E, [ E>=2 && E>=B && A>=2+F && 2+F-A+E>=2 ], cost: 1/2-3/2*F-(1+F-A)*E+3/2*A+E-1/2*(1+F-A)^2
15.10/5.53	
15.10/5.53	     36: f15 -> f15 : E'=2+F-A+E, F'=A, G'=free_2, H'=3+F-A+E, [ E>=2 && B>=1+E && A>=2+F && 3+F-A+E>=2 ], cost: 1/2-3/2*F-(1+F-A)*(1+E)+3/2*A+E-1/2*(1+F-A)^2
15.10/5.53	
15.10/5.53	     37: f15 -> f15 : E'=1, F'=F+E, G'=free_2, H'=2, [ E>=2 && E>=B && A>=2+F && A>=F+E ], cost: 1/2+(-1+E)*E+5/2*E-1/2*(-1+E)^2
15.10/5.53	
15.10/5.53	     38: f15 -> f15 : E'=1, F'=1+F+E, G'=free_2, H'=2, [ E>=2 && B>=1+E && A>=2+F && A>=1+F+E ], cost: 2-1/2*E^2+(1+E)*E+5/2*E
15.10/5.53	
15.10/5.53	     39: f15 -> [7] : [ A>=1+F && E>=2 ], cost: 1+E
15.10/5.53	
15.10/5.53	     40: f15 -> f15 : F'=A, G'=free_2, H'=E, [ A>=1+F && E>=2 && E>=B ], cost: -2*F+2*A-(F-A)*E
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Chained accelerated rules (with incoming rules):
15.10/5.53	
15.10/5.53	   Start location: f0
15.10/5.53	
15.10/5.53	      0: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=free, F'=0, [], cost: 1
15.10/5.53	
15.10/5.53	     18: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=-10+free, F'=10, G'=free_1, H'=1, [ 1>=free ], cost: 21
15.10/5.53	
15.10/5.53	     21: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=-10+free, F'=10, G'=free_2, H'=-9+free, [ -9+free>=2 ], cost: -34+10*free
15.10/5.53	
15.10/5.53	     24: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=1, F'=-1+free, G'=free_2, H'=2, [ free>=2 && 10>=-1+free ], cost: -1/2-1/2*(-1+free)^2+free*(-1+free)+3/2*free
15.10/5.53	
15.10/5.53	     41: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=-9+free, F'=10, G'=free_2, H'=-8+free, [ free>=35 ], cost: -24+10*free
15.10/5.53	
15.10/5.53	     42: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=-8+free, F'=10, G'=free_2, H'=-7+free, [ 35>=1+free && -7+free>=2 ], cost: -15+10*free
15.10/5.53	
15.10/5.53	     43: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=1, F'=1+free, G'=free_2, H'=2, [ free>=2 && 10>=1+free ], cost: 3-1/2*free^2+(1+free)*free+5/2*free
15.10/5.53	
15.10/5.53	     44: f0 -> f15 : A'=10, B'=35, C'=285, D'=free, E'=free, F'=10, G'=free_2, H'=free, [ free>=35 ], cost: 21+10*free
15.10/5.53	
15.10/5.53	     39: f15 -> [7] : [ A>=1+F && E>=2 ], cost: 1+E
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Eliminated locations (on tree-shaped paths):
15.10/5.53	
15.10/5.53	   Start location: f0
15.10/5.53	
15.10/5.53	     45: f0 -> [7] : A'=10, B'=35, C'=285, D'=free, E'=free, F'=0, [ free>=2 ], cost: 2+free
15.10/5.53	
15.10/5.53	     46: f0 -> [9] : [ -9+free>=2 ], cost: -34+10*free
15.10/5.53	
15.10/5.53	     47: f0 -> [9] : [ free>=2 && 10>=-1+free ], cost: -1/2-1/2*(-1+free)^2+free*(-1+free)+3/2*free
15.10/5.53	
15.10/5.53	     48: f0 -> [9] : [ free>=35 ], cost: -24+10*free
15.10/5.53	
15.10/5.53	     49: f0 -> [9] : [ 35>=1+free && -7+free>=2 ], cost: -15+10*free
15.10/5.53	
15.10/5.53	     50: f0 -> [9] : [ free>=2 && 10>=1+free ], cost: 3-1/2*free^2+(1+free)*free+5/2*free
15.10/5.53	
15.10/5.53	     51: f0 -> [9] : [ free>=35 ], cost: 21+10*free
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	### Computing asymptotic complexity ###
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Fully simplified ITS problem
15.10/5.53	
15.10/5.53	   Start location: f0
15.10/5.53	
15.10/5.53	     45: f0 -> [7] : A'=10, B'=35, C'=285, D'=free, E'=free, F'=0, [ free>=2 ], cost: 2+free
15.10/5.53	
15.10/5.53	     46: f0 -> [9] : [ -9+free>=2 ], cost: -34+10*free
15.10/5.53	
15.10/5.53	     47: f0 -> [9] : [ free>=2 && 10>=-1+free ], cost: -1/2-1/2*(-1+free)^2+free*(-1+free)+3/2*free
15.10/5.53	
15.10/5.53	     49: f0 -> [9] : [ 35>=1+free && -7+free>=2 ], cost: -15+10*free
15.10/5.53	
15.10/5.53	     50: f0 -> [9] : [ free>=2 && 10>=1+free ], cost: 3-1/2*free^2+(1+free)*free+5/2*free
15.10/5.53	
15.10/5.53	     51: f0 -> [9] : [ free>=35 ], cost: 21+10*free
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Computing asymptotic complexity for rule 45
15.10/5.53	
15.10/5.53	   Solved the limit problem by the following transformations:
15.10/5.53	
15.10/5.53	      Created initial limit problem:
15.10/5.53	
15.10/5.53	      2+free (+), -1+free (+/+!) [not solved]
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	      removing all constraints (solved by SMT)
15.10/5.53	
15.10/5.53	      resulting limit problem: [solved]
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	      applying transformation rule (C) using substitution {free==n}
15.10/5.53	
15.10/5.53	      resulting limit problem:
15.10/5.53	
15.10/5.53	      [solved]
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	   Solution:
15.10/5.53	
15.10/5.53	      free / n
15.10/5.53	
15.10/5.53	   Resulting cost 2+n has complexity: Unbounded
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Found new complexity Unbounded.
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	Obtained the following overall complexity (w.r.t. the length of the input n):
15.10/5.53	
15.10/5.53	   Complexity:  Unbounded
15.10/5.53	
15.10/5.53	   Cpx degree:  Unbounded
15.10/5.53	
15.10/5.53	   Solved cost: 2+n
15.10/5.53	
15.10/5.53	   Rule cost:   2+free
15.10/5.53	
15.10/5.53	   Rule guard:  [ free>=2 ]
15.10/5.53	
15.10/5.53	
15.10/5.53	
15.10/5.53	WORST_CASE(INF,?)
15.10/5.53	
15.10/5.53	
15.10/5.53	----------------------------------------
15.10/5.53	
15.10/5.53	(2)
15.10/5.53	BOUNDS(INF, INF)
15.35/5.55	EOF