3.27/1.98	WORST_CASE(NON_POLY, ?)
3.98/1.99	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.98/1.99	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.98/1.99	
3.98/1.99	
3.98/1.99	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.98/1.99	
3.98/1.99	(0) CpxIntTrs
3.98/1.99	(1) Loat Proof [FINISHED, 317 ms]
3.98/1.99	(2) BOUNDS(INF, INF)
3.98/1.99	
3.98/1.99	
3.98/1.99	----------------------------------------
3.98/1.99	
3.98/1.99	(0)
3.98/1.99	Obligation:
3.98/1.99	Complexity Int TRS consisting of the following rules:
3.98/1.99	f9(A, B, C, D) -> Com_1(f15(A, 0, E, D)) :|: 0 >= A && E >= 1
3.98/1.99	f15(A, B, C, D) -> Com_1(f15(A, B, C, D)) :|: C >= 1
3.98/1.99	f23(A, B, C, D) -> Com_1(f23(A, B, C, D)) :|: TRUE
3.98/1.99	f25(A, B, C, D) -> Com_1(f28(A, B, C, D)) :|: TRUE
3.98/1.99	f15(A, B, C, D) -> Com_1(f9(E, B, C, 0)) :|: 0 >= C
3.98/1.99	f9(A, B, C, D) -> Com_1(f23(A, B, C, D)) :|: A >= 1
3.98/1.99	f0(A, B, C, D) -> Com_1(f9(E, 0, C, 0)) :|: TRUE
3.98/1.99	
3.98/1.99	The start-symbols are:[f0_4]
3.98/1.99	
3.98/1.99	
3.98/1.99	----------------------------------------
3.98/1.99	
3.98/1.99	(1) Loat Proof (FINISHED)
3.98/1.99	
3.98/1.99	
3.98/1.99	### Pre-processing the ITS problem ###
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	Initial linear ITS problem
3.98/1.99	
3.98/1.99	   Start location: f0
3.98/1.99	
3.98/1.99	      0: f9 -> f15 : B'=0, C'=free, [ 0>=A && free>=1 ], cost: 1
3.98/1.99	
3.98/1.99	      5: f9 -> f23 : [ A>=1 ], cost: 1
3.98/1.99	
3.98/1.99	      1: f15 -> f15 : [ C>=1 ], cost: 1
3.98/1.99	
3.98/1.99	      4: f15 -> f9 : A'=free_1, D'=0, [ 0>=C ], cost: 1
3.98/1.99	
3.98/1.99	      2: f23 -> f23 : [], cost: 1
3.98/1.99	
3.98/1.99	      3: f25 -> f28 : [], cost: 1
3.98/1.99	
3.98/1.99	      6: f0 -> f9 : A'=free_2, B'=0, D'=0, [], cost: 1
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	Removed unreachable and leaf rules:
3.98/1.99	
3.98/1.99	   Start location: f0
3.98/1.99	
3.98/1.99	      0: f9 -> f15 : B'=0, C'=free, [ 0>=A && free>=1 ], cost: 1
3.98/1.99	
3.98/1.99	      5: f9 -> f23 : [ A>=1 ], cost: 1
3.98/1.99	
3.98/1.99	      1: f15 -> f15 : [ C>=1 ], cost: 1
3.98/1.99	
3.98/1.99	      4: f15 -> f9 : A'=free_1, D'=0, [ 0>=C ], cost: 1
3.98/1.99	
3.98/1.99	      2: f23 -> f23 : [], cost: 1
3.98/1.99	
3.98/1.99	      6: f0 -> f9 : A'=free_2, B'=0, D'=0, [], cost: 1
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	### Simplification by acceleration and chaining ###
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	Accelerating simple loops of location 1.
3.98/1.99	
3.98/1.99	   Accelerating the following rules:
3.98/1.99	
3.98/1.99	      1: f15 -> f15 : [ C>=1 ], cost: 1
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	   Accelerated rule 1 with NONTERM, yielding the new rule 7.
3.98/1.99	
3.98/1.99	   Removing the simple loops: 1.
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	Accelerating simple loops of location 2.
3.98/1.99	
3.98/1.99	   Accelerating the following rules:
3.98/1.99	
3.98/1.99	      2: f23 -> f23 : [], cost: 1
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	   Accelerated rule 2 with NONTERM, yielding the new rule 8.
3.98/1.99	
3.98/1.99	   Removing the simple loops: 2.
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	Accelerated all simple loops using metering functions (where possible):
3.98/1.99	
3.98/1.99	   Start location: f0
3.98/1.99	
3.98/1.99	      0: f9 -> f15 : B'=0, C'=free, [ 0>=A && free>=1 ], cost: 1
3.98/1.99	
3.98/1.99	      5: f9 -> f23 : [ A>=1 ], cost: 1
3.98/1.99	
3.98/1.99	      4: f15 -> f9 : A'=free_1, D'=0, [ 0>=C ], cost: 1
3.98/1.99	
3.98/1.99	      7: f15 -> [6] : [ C>=1 ], cost: INF
3.98/1.99	
3.98/1.99	      8: f23 -> [7] : [], cost: INF
3.98/1.99	
3.98/1.99	      6: f0 -> f9 : A'=free_2, B'=0, D'=0, [], cost: 1
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	Chained accelerated rules (with incoming rules):
3.98/1.99	
3.98/1.99	   Start location: f0
3.98/1.99	
3.98/1.99	      0: f9 -> f15 : B'=0, C'=free, [ 0>=A && free>=1 ], cost: 1
3.98/1.99	
3.98/1.99	      5: f9 -> f23 : [ A>=1 ], cost: 1
3.98/1.99	
3.98/1.99	      9: f9 -> [6] : B'=0, C'=free, [ 0>=A && free>=1 ], cost: INF
3.98/1.99	
3.98/1.99	     10: f9 -> [7] : [ A>=1 ], cost: INF
3.98/1.99	
3.98/1.99	      4: f15 -> f9 : A'=free_1, D'=0, [ 0>=C ], cost: 1
3.98/1.99	
3.98/1.99	      6: f0 -> f9 : A'=free_2, B'=0, D'=0, [], cost: 1
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	Removed unreachable locations (and leaf rules with constant cost):
3.98/1.99	
3.98/1.99	   Start location: f0
3.98/1.99	
3.98/1.99	      0: f9 -> f15 : B'=0, C'=free, [ 0>=A && free>=1 ], cost: 1
3.98/1.99	
3.98/1.99	      9: f9 -> [6] : B'=0, C'=free, [ 0>=A && free>=1 ], cost: INF
3.98/1.99	
3.98/1.99	     10: f9 -> [7] : [ A>=1 ], cost: INF
3.98/1.99	
3.98/1.99	      4: f15 -> f9 : A'=free_1, D'=0, [ 0>=C ], cost: 1
3.98/1.99	
3.98/1.99	      6: f0 -> f9 : A'=free_2, B'=0, D'=0, [], cost: 1
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	Eliminated locations (on linear paths):
3.98/1.99	
3.98/1.99	   Start location: f0
3.98/1.99	
3.98/1.99	      9: f9 -> [6] : B'=0, C'=free, [ 0>=A && free>=1 ], cost: INF
3.98/1.99	
3.98/1.99	     10: f9 -> [7] : [ A>=1 ], cost: INF
3.98/1.99	
3.98/1.99	      6: f0 -> f9 : A'=free_2, B'=0, D'=0, [], cost: 1
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	Eliminated locations (on tree-shaped paths):
3.98/1.99	
3.98/1.99	   Start location: f0
3.98/1.99	
3.98/1.99	     11: f0 -> [6] : A'=free_2, B'=0, C'=free, D'=0, [ 0>=free_2 && free>=1 ], cost: INF
3.98/1.99	
3.98/1.99	     12: f0 -> [7] : A'=free_2, B'=0, D'=0, [ free_2>=1 ], cost: INF
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	### Computing asymptotic complexity ###
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	Fully simplified ITS problem
3.98/1.99	
3.98/1.99	   Start location: f0
3.98/1.99	
3.98/1.99	     11: f0 -> [6] : A'=free_2, B'=0, C'=free, D'=0, [ 0>=free_2 && free>=1 ], cost: INF
3.98/1.99	
3.98/1.99	     12: f0 -> [7] : A'=free_2, B'=0, D'=0, [ free_2>=1 ], cost: INF
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	Computing asymptotic complexity for rule 11
3.98/1.99	
3.98/1.99	   Resulting cost INF has complexity: Nonterm
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	Found new complexity Nonterm.
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	Obtained the following overall complexity (w.r.t. the length of the input n):
3.98/1.99	
3.98/1.99	   Complexity:  Nonterm
3.98/1.99	
3.98/1.99	   Cpx degree:  Nonterm
3.98/1.99	
3.98/1.99	   Solved cost: INF
3.98/1.99	
3.98/1.99	   Rule cost:   INF
3.98/1.99	
3.98/1.99	   Rule guard:  [ 0>=free_2 && free>=1 ]
3.98/1.99	
3.98/1.99	
3.98/1.99	
3.98/1.99	NO
3.98/1.99	
3.98/1.99	
3.98/1.99	----------------------------------------
3.98/1.99	
3.98/1.99	(2)
3.98/1.99	BOUNDS(INF, INF)
3.98/2.00	EOF