4.47/2.11	WORST_CASE(NON_POLY, ?)
4.47/2.11	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.47/2.11	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.47/2.11	
4.47/2.11	
4.47/2.11	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
4.47/2.11	
4.47/2.11	(0) CpxIntTrs
4.47/2.11	(1) Loat Proof [FINISHED, 415 ms]
4.47/2.11	(2) BOUNDS(INF, INF)
4.47/2.11	
4.47/2.11	
4.47/2.11	----------------------------------------
4.47/2.11	
4.47/2.11	(0)
4.47/2.11	Obligation:
4.47/2.11	Complexity Int TRS consisting of the following rules:
4.47/2.11	f10(A, B, C, D, E, F) -> Com_1(f16(A, 0, G, G, E, F)) :|: 0 >= A
4.47/2.11	f16(A, B, C, D, E, F) -> Com_1(f16(A, B, C, D, E, F)) :|: D >= 1
4.47/2.11	f25(A, B, C, D, E, F) -> Com_1(f25(A, B, C, D, E, F)) :|: TRUE
4.47/2.11	f27(A, B, C, D, E, F) -> Com_1(f30(A, B, C, D, E, F)) :|: TRUE
4.47/2.11	f16(A, B, C, D, E, F) -> Com_1(f10(G, B, C, D, 0, G)) :|: 0 >= D
4.47/2.11	f10(A, B, C, D, E, F) -> Com_1(f25(A, B, C, D, E, F)) :|: A >= 1
4.47/2.11	f0(A, B, C, D, E, F) -> Com_1(f10(G, 0, C, D, 0, G)) :|: TRUE
4.47/2.11	
4.47/2.11	The start-symbols are:[f0_6]
4.47/2.11	
4.47/2.11	
4.47/2.11	----------------------------------------
4.47/2.11	
4.47/2.11	(1) Loat Proof (FINISHED)
4.47/2.11	
4.47/2.11	
4.47/2.11	### Pre-processing the ITS problem ###
4.47/2.11	
4.47/2.11	
4.47/2.11	
4.47/2.11	Initial linear ITS problem
4.47/2.11	
4.47/2.11	   Start location: f0
4.47/2.11	
4.47/2.11	      0: f10 -> f16 : B'=0, C'=free, D'=free, [ 0>=A ], cost: 1
4.47/2.11	
4.47/2.11	      5: f10 -> f25 : [ A>=1 ], cost: 1
4.47/2.11	
4.47/2.11	      1: f16 -> f16 : [ D>=1 ], cost: 1
4.47/2.11	
4.47/2.11	      4: f16 -> f10 : A'=free_1, E'=0, F'=free_1, [ 0>=D ], cost: 1
4.47/2.11	
4.47/2.11	      2: f25 -> f25 : [], cost: 1
4.47/2.11	
4.47/2.11	      3: f27 -> f30 : [], cost: 1
4.47/2.11	
4.47/2.11	      6: f0 -> f10 : A'=free_2, B'=0, E'=0, F'=free_2, [], cost: 1
4.47/2.11	
4.47/2.11	
4.47/2.11	
4.47/2.11	Removed unreachable and leaf rules:
4.47/2.11	
4.47/2.11	   Start location: f0
4.47/2.11	
4.47/2.11	      0: f10 -> f16 : B'=0, C'=free, D'=free, [ 0>=A ], cost: 1
4.47/2.11	
4.47/2.11	      5: f10 -> f25 : [ A>=1 ], cost: 1
4.47/2.11	
4.47/2.11	      1: f16 -> f16 : [ D>=1 ], cost: 1
4.47/2.11	
4.47/2.11	      4: f16 -> f10 : A'=free_1, E'=0, F'=free_1, [ 0>=D ], cost: 1
4.47/2.11	
4.47/2.11	      2: f25 -> f25 : [], cost: 1
4.47/2.11	
4.47/2.11	      6: f0 -> f10 : A'=free_2, B'=0, E'=0, F'=free_2, [], cost: 1
4.47/2.11	
4.47/2.11	
4.47/2.11	
4.47/2.11	### Simplification by acceleration and chaining ###
4.47/2.11	
4.47/2.11	
4.47/2.11	
4.47/2.11	Accelerating simple loops of location 1.
4.47/2.11	
4.47/2.11	   Accelerating the following rules:
4.47/2.11	
4.47/2.11	      1: f16 -> f16 : [ D>=1 ], cost: 1
4.47/2.11	
4.47/2.11	
4.47/2.11	
4.47/2.11	   Accelerated rule 1 with NONTERM, yielding the new rule 7.
4.47/2.11	
4.47/2.11	   Removing the simple loops: 1.
4.47/2.11	
4.47/2.11	
4.47/2.11	
4.47/2.11	Accelerating simple loops of location 2.
4.47/2.11	
4.47/2.11	   Accelerating the following rules:
4.47/2.11	
4.47/2.11	      2: f25 -> f25 : [], cost: 1
4.47/2.11	
4.47/2.11	
4.47/2.11	
4.47/2.11	   Accelerated rule 2 with NONTERM, yielding the new rule 8.
4.47/2.11	
4.47/2.11	   Removing the simple loops: 2.
4.47/2.11	
4.47/2.11	
4.47/2.11	
4.47/2.11	Accelerated all simple loops using metering functions (where possible):
4.47/2.11	
4.47/2.11	   Start location: f0
4.47/2.11	
4.47/2.11	      0: f10 -> f16 : B'=0, C'=free, D'=free, [ 0>=A ], cost: 1
4.47/2.11	
4.47/2.11	      5: f10 -> f25 : [ A>=1 ], cost: 1
4.47/2.11	
4.47/2.11	      4: f16 -> f10 : A'=free_1, E'=0, F'=free_1, [ 0>=D ], cost: 1
4.47/2.11	
4.47/2.11	      7: f16 -> [6] : [ D>=1 ], cost: INF
4.47/2.11	
4.47/2.11	      8: f25 -> [7] : [], cost: INF
4.47/2.11	
4.47/2.11	      6: f0 -> f10 : A'=free_2, B'=0, E'=0, F'=free_2, [], cost: 1
4.47/2.11	
4.47/2.11	
4.47/2.11	
4.47/2.11	Chained accelerated rules (with incoming rules):
4.47/2.11	
4.47/2.11	   Start location: f0
4.47/2.11	
4.47/2.11	      0: f10 -> f16 : B'=0, C'=free, D'=free, [ 0>=A ], cost: 1
4.47/2.11	
4.47/2.11	      5: f10 -> f25 : [ A>=1 ], cost: 1
4.47/2.11	
4.47/2.11	      9: f10 -> [6] : B'=0, C'=free, D'=free, [ 0>=A && free>=1 ], cost: INF
4.47/2.11	
4.47/2.11	     10: f10 -> [7] : [ A>=1 ], cost: INF
4.47/2.11	
4.47/2.11	      4: f16 -> f10 : A'=free_1, E'=0, F'=free_1, [ 0>=D ], cost: 1
4.47/2.11	
4.47/2.11	      6: f0 -> f10 : A'=free_2, B'=0, E'=0, F'=free_2, [], cost: 1
4.47/2.11	
4.47/2.11	
4.47/2.11	
4.47/2.11	Removed unreachable locations (and leaf rules with constant cost):
4.47/2.11	
4.47/2.11	   Start location: f0
4.47/2.11	
4.47/2.11	      0: f10 -> f16 : B'=0, C'=free, D'=free, [ 0>=A ], cost: 1
4.47/2.11	
4.47/2.11	      9: f10 -> [6] : B'=0, C'=free, D'=free, [ 0>=A && free>=1 ], cost: INF
4.47/2.11	
4.47/2.11	     10: f10 -> [7] : [ A>=1 ], cost: INF
4.47/2.11	
4.47/2.11	      4: f16 -> f10 : A'=free_1, E'=0, F'=free_1, [ 0>=D ], cost: 1
4.47/2.11	
4.47/2.11	      6: f0 -> f10 : A'=free_2, B'=0, E'=0, F'=free_2, [], cost: 1
4.47/2.11	
4.47/2.11	
4.47/2.11	
4.47/2.11	Eliminated locations (on linear paths):
4.47/2.11	
4.47/2.11	   Start location: f0
4.47/2.11	
4.47/2.11	      9: f10 -> [6] : B'=0, C'=free, D'=free, [ 0>=A && free>=1 ], cost: INF
4.47/2.11	
4.47/2.11	     10: f10 -> [7] : [ A>=1 ], cost: INF
4.47/2.11	
4.47/2.11	     11: f10 -> f10 : A'=free_1, B'=0, C'=free, D'=free, E'=0, F'=free_1, [ 0>=A && 0>=free ], cost: 2
4.47/2.11	
4.47/2.11	      6: f0 -> f10 : A'=free_2, B'=0, E'=0, F'=free_2, [], cost: 1
4.47/2.11	
4.47/2.11	
4.47/2.11	
4.47/2.11	Accelerating simple loops of location 0.
4.47/2.11	
4.47/2.11	   Accelerating the following rules:
4.47/2.11	
4.47/2.11	     11: f10 -> f10 : A'=free_1, B'=0, C'=free, D'=free, E'=0, F'=free_1, [ 0>=A && 0>=free ], cost: 2
4.47/2.12	
4.47/2.12	
4.47/2.12	
4.47/2.12	   Accelerated rule 11 with NONTERM (after strengthening guard), yielding the new rule 12.
4.47/2.12	
4.47/2.12	   Removing the simple loops:.
4.47/2.12	
4.47/2.12	
4.47/2.12	
4.47/2.12	Accelerated all simple loops using metering functions (where possible):
4.47/2.12	
4.47/2.12	   Start location: f0
4.47/2.12	
4.47/2.12	      9: f10 -> [6] : B'=0, C'=free, D'=free, [ 0>=A && free>=1 ], cost: INF
4.47/2.12	
4.47/2.12	     10: f10 -> [7] : [ A>=1 ], cost: INF
4.47/2.12	
4.47/2.12	     11: f10 -> f10 : A'=free_1, B'=0, C'=free, D'=free, E'=0, F'=free_1, [ 0>=A && 0>=free ], cost: 2
4.47/2.12	
4.47/2.12	     12: f10 -> [8] : [ 0>=A && 0>=free && 0>=free_1 ], cost: INF
4.47/2.12	
4.47/2.12	      6: f0 -> f10 : A'=free_2, B'=0, E'=0, F'=free_2, [], cost: 1
4.47/2.12	
4.47/2.12	
4.47/2.12	
4.47/2.12	Chained accelerated rules (with incoming rules):
4.47/2.12	
4.47/2.12	   Start location: f0
4.47/2.12	
4.47/2.12	      9: f10 -> [6] : B'=0, C'=free, D'=free, [ 0>=A && free>=1 ], cost: INF
4.47/2.12	
4.47/2.12	     10: f10 -> [7] : [ A>=1 ], cost: INF
4.47/2.12	
4.47/2.12	      6: f0 -> f10 : A'=free_2, B'=0, E'=0, F'=free_2, [], cost: 1
4.47/2.12	
4.47/2.12	     13: f0 -> f10 : A'=free_1, B'=0, C'=free, D'=free, E'=0, F'=free_1, [ 0>=free ], cost: 3
4.47/2.12	
4.47/2.12	     14: f0 -> [8] : A'=free_2, B'=0, E'=0, F'=free_2, [ 0>=free_2 ], cost: INF
4.47/2.12	
4.47/2.12	
4.47/2.12	
4.47/2.12	Eliminated locations (on tree-shaped paths):
4.47/2.12	
4.47/2.12	   Start location: f0
4.47/2.12	
4.47/2.12	     14: f0 -> [8] : A'=free_2, B'=0, E'=0, F'=free_2, [ 0>=free_2 ], cost: INF
4.47/2.12	
4.47/2.12	     15: f0 -> [6] : A'=free_2, B'=0, C'=free, D'=free, E'=0, F'=free_2, [ 0>=free_2 && free>=1 ], cost: INF
4.47/2.12	
4.47/2.12	     16: f0 -> [7] : A'=free_2, B'=0, E'=0, F'=free_2, [ free_2>=1 ], cost: INF
4.47/2.12	
4.47/2.12	     17: f0 -> [7] : A'=free_1, B'=0, C'=free, D'=free, E'=0, F'=free_1, [ 0>=free && free_1>=1 ], cost: INF
4.47/2.12	
4.47/2.12	
4.47/2.12	
4.47/2.12	### Computing asymptotic complexity ###
4.47/2.12	
4.47/2.12	
4.47/2.12	
4.47/2.12	Fully simplified ITS problem
4.47/2.12	
4.47/2.12	   Start location: f0
4.47/2.12	
4.47/2.12	     14: f0 -> [8] : A'=free_2, B'=0, E'=0, F'=free_2, [ 0>=free_2 ], cost: INF
4.47/2.12	
4.47/2.12	     15: f0 -> [6] : A'=free_2, B'=0, C'=free, D'=free, E'=0, F'=free_2, [ 0>=free_2 && free>=1 ], cost: INF
4.47/2.12	
4.47/2.12	     16: f0 -> [7] : A'=free_2, B'=0, E'=0, F'=free_2, [ free_2>=1 ], cost: INF
4.47/2.12	
4.47/2.12	     17: f0 -> [7] : A'=free_1, B'=0, C'=free, D'=free, E'=0, F'=free_1, [ 0>=free && free_1>=1 ], cost: INF
4.47/2.12	
4.47/2.12	
4.47/2.12	
4.47/2.12	Computing asymptotic complexity for rule 14
4.47/2.12	
4.47/2.12	   Resulting cost INF has complexity: Nonterm
4.47/2.12	
4.47/2.12	
4.47/2.12	
4.47/2.12	Found new complexity Nonterm.
4.47/2.12	
4.47/2.12	
4.47/2.12	
4.47/2.12	Obtained the following overall complexity (w.r.t. the length of the input n):
4.47/2.12	
4.47/2.12	   Complexity:  Nonterm
4.47/2.12	
4.47/2.12	   Cpx degree:  Nonterm
4.47/2.12	
4.47/2.12	   Solved cost: INF
4.47/2.12	
4.47/2.12	   Rule cost:   INF
4.47/2.12	
4.47/2.12	   Rule guard:  [ 0>=free_2 ]
4.47/2.12	
4.47/2.12	
4.47/2.12	
4.47/2.12	NO
4.47/2.12	
4.47/2.12	
4.47/2.12	----------------------------------------
4.47/2.12	
4.47/2.12	(2)
4.47/2.12	BOUNDS(INF, INF)
4.47/2.13	EOF