4.25/2.09	WORST_CASE(NON_POLY, ?)
4.40/2.10	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.40/2.10	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.40/2.10	
4.40/2.10	
4.40/2.10	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
4.40/2.10	
4.40/2.10	(0) CpxIntTrs
4.40/2.10	(1) Loat Proof [FINISHED, 424 ms]
4.40/2.10	(2) BOUNDS(INF, INF)
4.40/2.10	
4.40/2.10	
4.40/2.10	----------------------------------------
4.40/2.10	
4.40/2.10	(0)
4.40/2.10	Obligation:
4.40/2.10	Complexity Int TRS consisting of the following rules:
4.40/2.10	f10(A, B, C, D, E) -> Com_1(f16(A, 0, F, F, E)) :|: 0 >= A
4.40/2.10	f16(A, B, C, D, E) -> Com_1(f16(A, B, C, D, E)) :|: D >= 1
4.40/2.10	f25(A, B, C, D, E) -> Com_1(f25(A, B, C, D, E)) :|: TRUE
4.40/2.10	f27(A, B, C, D, E) -> Com_1(f30(A, B, C, D, E)) :|: TRUE
4.40/2.10	f16(A, B, C, D, E) -> Com_1(f10(F, B, F, D, 0)) :|: 0 >= D
4.40/2.10	f10(A, B, C, D, E) -> Com_1(f25(A, B, C, D, E)) :|: A >= 1
4.40/2.10	f0(A, B, C, D, E) -> Com_1(f10(F, 0, F, D, 0)) :|: TRUE
4.40/2.10	
4.40/2.10	The start-symbols are:[f0_5]
4.40/2.10	
4.40/2.10	
4.40/2.10	----------------------------------------
4.40/2.10	
4.40/2.10	(1) Loat Proof (FINISHED)
4.40/2.10	
4.40/2.10	
4.40/2.10	### Pre-processing the ITS problem ###
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	Initial linear ITS problem
4.40/2.10	
4.40/2.10	   Start location: f0
4.40/2.10	
4.40/2.10	      0: f10 -> f16 : B'=0, C'=free, D'=free, [ 0>=A ], cost: 1
4.40/2.10	
4.40/2.10	      5: f10 -> f25 : [ A>=1 ], cost: 1
4.40/2.10	
4.40/2.10	      1: f16 -> f16 : [ D>=1 ], cost: 1
4.40/2.10	
4.40/2.10	      4: f16 -> f10 : A'=free_1, C'=free_1, E'=0, [ 0>=D ], cost: 1
4.40/2.10	
4.40/2.10	      2: f25 -> f25 : [], cost: 1
4.40/2.10	
4.40/2.10	      3: f27 -> f30 : [], cost: 1
4.40/2.10	
4.40/2.10	      6: f0 -> f10 : A'=free_2, B'=0, C'=free_2, E'=0, [], cost: 1
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	Removed unreachable and leaf rules:
4.40/2.10	
4.40/2.10	   Start location: f0
4.40/2.10	
4.40/2.10	      0: f10 -> f16 : B'=0, C'=free, D'=free, [ 0>=A ], cost: 1
4.40/2.10	
4.40/2.10	      5: f10 -> f25 : [ A>=1 ], cost: 1
4.40/2.10	
4.40/2.10	      1: f16 -> f16 : [ D>=1 ], cost: 1
4.40/2.10	
4.40/2.10	      4: f16 -> f10 : A'=free_1, C'=free_1, E'=0, [ 0>=D ], cost: 1
4.40/2.10	
4.40/2.10	      2: f25 -> f25 : [], cost: 1
4.40/2.10	
4.40/2.10	      6: f0 -> f10 : A'=free_2, B'=0, C'=free_2, E'=0, [], cost: 1
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	### Simplification by acceleration and chaining ###
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	Accelerating simple loops of location 1.
4.40/2.10	
4.40/2.10	   Accelerating the following rules:
4.40/2.10	
4.40/2.10	      1: f16 -> f16 : [ D>=1 ], cost: 1
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	   Accelerated rule 1 with NONTERM, yielding the new rule 7.
4.40/2.10	
4.40/2.10	   Removing the simple loops: 1.
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	Accelerating simple loops of location 2.
4.40/2.10	
4.40/2.10	   Accelerating the following rules:
4.40/2.10	
4.40/2.10	      2: f25 -> f25 : [], cost: 1
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	   Accelerated rule 2 with NONTERM, yielding the new rule 8.
4.40/2.10	
4.40/2.10	   Removing the simple loops: 2.
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	Accelerated all simple loops using metering functions (where possible):
4.40/2.10	
4.40/2.10	   Start location: f0
4.40/2.10	
4.40/2.10	      0: f10 -> f16 : B'=0, C'=free, D'=free, [ 0>=A ], cost: 1
4.40/2.10	
4.40/2.10	      5: f10 -> f25 : [ A>=1 ], cost: 1
4.40/2.10	
4.40/2.10	      4: f16 -> f10 : A'=free_1, C'=free_1, E'=0, [ 0>=D ], cost: 1
4.40/2.10	
4.40/2.10	      7: f16 -> [6] : [ D>=1 ], cost: INF
4.40/2.10	
4.40/2.10	      8: f25 -> [7] : [], cost: INF
4.40/2.10	
4.40/2.10	      6: f0 -> f10 : A'=free_2, B'=0, C'=free_2, E'=0, [], cost: 1
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	Chained accelerated rules (with incoming rules):
4.40/2.10	
4.40/2.10	   Start location: f0
4.40/2.10	
4.40/2.10	      0: f10 -> f16 : B'=0, C'=free, D'=free, [ 0>=A ], cost: 1
4.40/2.10	
4.40/2.10	      5: f10 -> f25 : [ A>=1 ], cost: 1
4.40/2.10	
4.40/2.10	      9: f10 -> [6] : B'=0, C'=free, D'=free, [ 0>=A && free>=1 ], cost: INF
4.40/2.10	
4.40/2.10	     10: f10 -> [7] : [ A>=1 ], cost: INF
4.40/2.10	
4.40/2.10	      4: f16 -> f10 : A'=free_1, C'=free_1, E'=0, [ 0>=D ], cost: 1
4.40/2.10	
4.40/2.10	      6: f0 -> f10 : A'=free_2, B'=0, C'=free_2, E'=0, [], cost: 1
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	Removed unreachable locations (and leaf rules with constant cost):
4.40/2.10	
4.40/2.10	   Start location: f0
4.40/2.10	
4.40/2.10	      0: f10 -> f16 : B'=0, C'=free, D'=free, [ 0>=A ], cost: 1
4.40/2.10	
4.40/2.10	      9: f10 -> [6] : B'=0, C'=free, D'=free, [ 0>=A && free>=1 ], cost: INF
4.40/2.10	
4.40/2.10	     10: f10 -> [7] : [ A>=1 ], cost: INF
4.40/2.10	
4.40/2.10	      4: f16 -> f10 : A'=free_1, C'=free_1, E'=0, [ 0>=D ], cost: 1
4.40/2.10	
4.40/2.10	      6: f0 -> f10 : A'=free_2, B'=0, C'=free_2, E'=0, [], cost: 1
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	Eliminated locations (on linear paths):
4.40/2.10	
4.40/2.10	   Start location: f0
4.40/2.10	
4.40/2.10	      9: f10 -> [6] : B'=0, C'=free, D'=free, [ 0>=A && free>=1 ], cost: INF
4.40/2.10	
4.40/2.10	     10: f10 -> [7] : [ A>=1 ], cost: INF
4.40/2.10	
4.40/2.10	     11: f10 -> f10 : A'=free_1, B'=0, C'=free_1, D'=free, E'=0, [ 0>=A && 0>=free ], cost: 2
4.40/2.10	
4.40/2.10	      6: f0 -> f10 : A'=free_2, B'=0, C'=free_2, E'=0, [], cost: 1
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	Accelerating simple loops of location 0.
4.40/2.10	
4.40/2.10	   Accelerating the following rules:
4.40/2.10	
4.40/2.10	     11: f10 -> f10 : A'=free_1, B'=0, C'=free_1, D'=free, E'=0, [ 0>=A && 0>=free ], cost: 2
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	   Accelerated rule 11 with NONTERM (after strengthening guard), yielding the new rule 12.
4.40/2.10	
4.40/2.10	   Removing the simple loops:.
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	Accelerated all simple loops using metering functions (where possible):
4.40/2.10	
4.40/2.10	   Start location: f0
4.40/2.10	
4.40/2.10	      9: f10 -> [6] : B'=0, C'=free, D'=free, [ 0>=A && free>=1 ], cost: INF
4.40/2.10	
4.40/2.10	     10: f10 -> [7] : [ A>=1 ], cost: INF
4.40/2.10	
4.40/2.10	     11: f10 -> f10 : A'=free_1, B'=0, C'=free_1, D'=free, E'=0, [ 0>=A && 0>=free ], cost: 2
4.40/2.10	
4.40/2.10	     12: f10 -> [8] : [ 0>=A && 0>=free && 0>=free_1 ], cost: INF
4.40/2.10	
4.40/2.10	      6: f0 -> f10 : A'=free_2, B'=0, C'=free_2, E'=0, [], cost: 1
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	Chained accelerated rules (with incoming rules):
4.40/2.10	
4.40/2.10	   Start location: f0
4.40/2.10	
4.40/2.10	      9: f10 -> [6] : B'=0, C'=free, D'=free, [ 0>=A && free>=1 ], cost: INF
4.40/2.10	
4.40/2.10	     10: f10 -> [7] : [ A>=1 ], cost: INF
4.40/2.10	
4.40/2.10	      6: f0 -> f10 : A'=free_2, B'=0, C'=free_2, E'=0, [], cost: 1
4.40/2.10	
4.40/2.10	     13: f0 -> f10 : A'=free_1, B'=0, C'=free_1, D'=free, E'=0, [ 0>=free ], cost: 3
4.40/2.10	
4.40/2.10	     14: f0 -> [8] : A'=free_2, B'=0, C'=free_2, E'=0, [ 0>=free_2 ], cost: INF
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	Eliminated locations (on tree-shaped paths):
4.40/2.10	
4.40/2.10	   Start location: f0
4.40/2.10	
4.40/2.10	     14: f0 -> [8] : A'=free_2, B'=0, C'=free_2, E'=0, [ 0>=free_2 ], cost: INF
4.40/2.10	
4.40/2.10	     15: f0 -> [6] : A'=free_2, B'=0, C'=free, D'=free, E'=0, [ 0>=free_2 && free>=1 ], cost: INF
4.40/2.10	
4.40/2.10	     16: f0 -> [7] : A'=free_2, B'=0, C'=free_2, E'=0, [ free_2>=1 ], cost: INF
4.40/2.10	
4.40/2.10	     17: f0 -> [7] : A'=free_1, B'=0, C'=free_1, D'=free, E'=0, [ 0>=free && free_1>=1 ], cost: INF
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	### Computing asymptotic complexity ###
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	Fully simplified ITS problem
4.40/2.10	
4.40/2.10	   Start location: f0
4.40/2.10	
4.40/2.10	     14: f0 -> [8] : A'=free_2, B'=0, C'=free_2, E'=0, [ 0>=free_2 ], cost: INF
4.40/2.10	
4.40/2.10	     15: f0 -> [6] : A'=free_2, B'=0, C'=free, D'=free, E'=0, [ 0>=free_2 && free>=1 ], cost: INF
4.40/2.10	
4.40/2.10	     16: f0 -> [7] : A'=free_2, B'=0, C'=free_2, E'=0, [ free_2>=1 ], cost: INF
4.40/2.10	
4.40/2.10	     17: f0 -> [7] : A'=free_1, B'=0, C'=free_1, D'=free, E'=0, [ 0>=free && free_1>=1 ], cost: INF
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	Computing asymptotic complexity for rule 14
4.40/2.10	
4.40/2.10	   Resulting cost INF has complexity: Nonterm
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	Found new complexity Nonterm.
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	Obtained the following overall complexity (w.r.t. the length of the input n):
4.40/2.10	
4.40/2.10	   Complexity:  Nonterm
4.40/2.10	
4.40/2.10	   Cpx degree:  Nonterm
4.40/2.10	
4.40/2.10	   Solved cost: INF
4.40/2.10	
4.40/2.10	   Rule cost:   INF
4.40/2.10	
4.40/2.10	   Rule guard:  [ 0>=free_2 ]
4.40/2.10	
4.40/2.10	
4.40/2.10	
4.40/2.10	NO
4.40/2.10	
4.40/2.10	
4.40/2.10	----------------------------------------
4.40/2.10	
4.40/2.10	(2)
4.40/2.10	BOUNDS(INF, INF)
4.40/2.12	EOF