4.20/1.92	WORST_CASE(NON_POLY, ?)
4.20/1.93	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.20/1.93	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.20/1.93	
4.20/1.93	
4.20/1.93	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
4.20/1.93	
4.20/1.93	(0) CpxIntTrs
4.20/1.93	(1) Loat Proof [FINISHED, 244 ms]
4.20/1.93	(2) BOUNDS(INF, INF)
4.20/1.93	
4.20/1.93	
4.20/1.93	----------------------------------------
4.20/1.93	
4.20/1.93	(0)
4.20/1.93	Obligation:
4.20/1.93	Complexity Int TRS consisting of the following rules:
4.20/1.93	f10(A, B, C, D, E) -> Com_1(f16(A, 0, F, D, E)) :|: 0 >= A && F >= 1
4.20/1.93	f16(A, B, C, D, E) -> Com_1(f16(A, B, C, D, E)) :|: C >= 1
4.20/1.93	f25(A, B, C, D, E) -> Com_1(f25(A, B, C, D, E)) :|: TRUE
4.20/1.93	f27(A, B, C, D, E) -> Com_1(f30(A, B, C, D, E)) :|: TRUE
4.20/1.93	f16(A, B, C, D, E) -> Com_1(f10(F, B, C, 0, F)) :|: 0 >= C
4.20/1.93	f10(A, B, C, D, E) -> Com_1(f25(A, B, C, D, E)) :|: A >= 1
4.20/1.93	f0(A, B, C, D, E) -> Com_1(f10(F, 0, C, 0, F)) :|: TRUE
4.20/1.93	
4.20/1.93	The start-symbols are:[f0_5]
4.20/1.93	
4.20/1.93	
4.20/1.93	----------------------------------------
4.20/1.93	
4.20/1.93	(1) Loat Proof (FINISHED)
4.20/1.93	
4.20/1.93	
4.20/1.93	### Pre-processing the ITS problem ###
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	Initial linear ITS problem
4.20/1.93	
4.20/1.93	   Start location: f0
4.20/1.93	
4.20/1.93	      0: f10 -> f16 : B'=0, C'=free, [ 0>=A && free>=1 ], cost: 1
4.20/1.93	
4.20/1.93	      5: f10 -> f25 : [ A>=1 ], cost: 1
4.20/1.93	
4.20/1.93	      1: f16 -> f16 : [ C>=1 ], cost: 1
4.20/1.93	
4.20/1.93	      4: f16 -> f10 : A'=free_1, D'=0, E'=free_1, [ 0>=C ], cost: 1
4.20/1.93	
4.20/1.93	      2: f25 -> f25 : [], cost: 1
4.20/1.93	
4.20/1.93	      3: f27 -> f30 : [], cost: 1
4.20/1.93	
4.20/1.93	      6: f0 -> f10 : A'=free_2, B'=0, D'=0, E'=free_2, [], cost: 1
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	Removed unreachable and leaf rules:
4.20/1.93	
4.20/1.93	   Start location: f0
4.20/1.93	
4.20/1.93	      0: f10 -> f16 : B'=0, C'=free, [ 0>=A && free>=1 ], cost: 1
4.20/1.93	
4.20/1.93	      5: f10 -> f25 : [ A>=1 ], cost: 1
4.20/1.93	
4.20/1.93	      1: f16 -> f16 : [ C>=1 ], cost: 1
4.20/1.93	
4.20/1.93	      4: f16 -> f10 : A'=free_1, D'=0, E'=free_1, [ 0>=C ], cost: 1
4.20/1.93	
4.20/1.93	      2: f25 -> f25 : [], cost: 1
4.20/1.93	
4.20/1.93	      6: f0 -> f10 : A'=free_2, B'=0, D'=0, E'=free_2, [], cost: 1
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	### Simplification by acceleration and chaining ###
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	Accelerating simple loops of location 1.
4.20/1.93	
4.20/1.93	   Accelerating the following rules:
4.20/1.93	
4.20/1.93	      1: f16 -> f16 : [ C>=1 ], cost: 1
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	   Accelerated rule 1 with NONTERM, yielding the new rule 7.
4.20/1.93	
4.20/1.93	   Removing the simple loops: 1.
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	Accelerating simple loops of location 2.
4.20/1.93	
4.20/1.93	   Accelerating the following rules:
4.20/1.93	
4.20/1.93	      2: f25 -> f25 : [], cost: 1
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	   Accelerated rule 2 with NONTERM, yielding the new rule 8.
4.20/1.93	
4.20/1.93	   Removing the simple loops: 2.
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	Accelerated all simple loops using metering functions (where possible):
4.20/1.93	
4.20/1.93	   Start location: f0
4.20/1.93	
4.20/1.93	      0: f10 -> f16 : B'=0, C'=free, [ 0>=A && free>=1 ], cost: 1
4.20/1.93	
4.20/1.93	      5: f10 -> f25 : [ A>=1 ], cost: 1
4.20/1.93	
4.20/1.93	      4: f16 -> f10 : A'=free_1, D'=0, E'=free_1, [ 0>=C ], cost: 1
4.20/1.93	
4.20/1.93	      7: f16 -> [6] : [ C>=1 ], cost: INF
4.20/1.93	
4.20/1.93	      8: f25 -> [7] : [], cost: INF
4.20/1.93	
4.20/1.93	      6: f0 -> f10 : A'=free_2, B'=0, D'=0, E'=free_2, [], cost: 1
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	Chained accelerated rules (with incoming rules):
4.20/1.93	
4.20/1.93	   Start location: f0
4.20/1.93	
4.20/1.93	      0: f10 -> f16 : B'=0, C'=free, [ 0>=A && free>=1 ], cost: 1
4.20/1.93	
4.20/1.93	      5: f10 -> f25 : [ A>=1 ], cost: 1
4.20/1.93	
4.20/1.93	      9: f10 -> [6] : B'=0, C'=free, [ 0>=A && free>=1 ], cost: INF
4.20/1.93	
4.20/1.93	     10: f10 -> [7] : [ A>=1 ], cost: INF
4.20/1.93	
4.20/1.93	      4: f16 -> f10 : A'=free_1, D'=0, E'=free_1, [ 0>=C ], cost: 1
4.20/1.93	
4.20/1.93	      6: f0 -> f10 : A'=free_2, B'=0, D'=0, E'=free_2, [], cost: 1
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	Removed unreachable locations (and leaf rules with constant cost):
4.20/1.93	
4.20/1.93	   Start location: f0
4.20/1.93	
4.20/1.93	      0: f10 -> f16 : B'=0, C'=free, [ 0>=A && free>=1 ], cost: 1
4.20/1.93	
4.20/1.93	      9: f10 -> [6] : B'=0, C'=free, [ 0>=A && free>=1 ], cost: INF
4.20/1.93	
4.20/1.93	     10: f10 -> [7] : [ A>=1 ], cost: INF
4.20/1.93	
4.20/1.93	      4: f16 -> f10 : A'=free_1, D'=0, E'=free_1, [ 0>=C ], cost: 1
4.20/1.93	
4.20/1.93	      6: f0 -> f10 : A'=free_2, B'=0, D'=0, E'=free_2, [], cost: 1
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	Eliminated locations (on linear paths):
4.20/1.93	
4.20/1.93	   Start location: f0
4.20/1.93	
4.20/1.93	      9: f10 -> [6] : B'=0, C'=free, [ 0>=A && free>=1 ], cost: INF
4.20/1.93	
4.20/1.93	     10: f10 -> [7] : [ A>=1 ], cost: INF
4.20/1.93	
4.20/1.93	      6: f0 -> f10 : A'=free_2, B'=0, D'=0, E'=free_2, [], cost: 1
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	Eliminated locations (on tree-shaped paths):
4.20/1.93	
4.20/1.93	   Start location: f0
4.20/1.93	
4.20/1.93	     11: f0 -> [6] : A'=free_2, B'=0, C'=free, D'=0, E'=free_2, [ 0>=free_2 && free>=1 ], cost: INF
4.20/1.93	
4.20/1.93	     12: f0 -> [7] : A'=free_2, B'=0, D'=0, E'=free_2, [ free_2>=1 ], cost: INF
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	### Computing asymptotic complexity ###
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	Fully simplified ITS problem
4.20/1.93	
4.20/1.93	   Start location: f0
4.20/1.93	
4.20/1.93	     11: f0 -> [6] : A'=free_2, B'=0, C'=free, D'=0, E'=free_2, [ 0>=free_2 && free>=1 ], cost: INF
4.20/1.93	
4.20/1.93	     12: f0 -> [7] : A'=free_2, B'=0, D'=0, E'=free_2, [ free_2>=1 ], cost: INF
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	Computing asymptotic complexity for rule 11
4.20/1.93	
4.20/1.93	   Resulting cost INF has complexity: Nonterm
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	Found new complexity Nonterm.
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	Obtained the following overall complexity (w.r.t. the length of the input n):
4.20/1.93	
4.20/1.93	   Complexity:  Nonterm
4.20/1.93	
4.20/1.93	   Cpx degree:  Nonterm
4.20/1.93	
4.20/1.93	   Solved cost: INF
4.20/1.93	
4.20/1.93	   Rule cost:   INF
4.20/1.93	
4.20/1.93	   Rule guard:  [ 0>=free_2 && free>=1 ]
4.20/1.93	
4.20/1.93	
4.20/1.93	
4.20/1.93	NO
4.20/1.93	
4.20/1.93	
4.20/1.93	----------------------------------------
4.20/1.93	
4.20/1.93	(2)
4.20/1.93	BOUNDS(INF, INF)
4.23/1.95	EOF