3.91/1.89	WORST_CASE(NON_POLY, ?)
3.91/1.89	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.91/1.89	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.91/1.89	
3.91/1.89	
3.91/1.89	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.91/1.89	
3.91/1.89	(0) CpxIntTrs
3.91/1.89	(1) Loat Proof [FINISHED, 216 ms]
3.91/1.89	(2) BOUNDS(INF, INF)
3.91/1.89	
3.91/1.89	
3.91/1.89	----------------------------------------
3.91/1.89	
3.91/1.89	(0)
3.91/1.89	Obligation:
3.91/1.89	Complexity Int TRS consisting of the following rules:
3.91/1.89	f4(A, B, C, D, E) -> Com_1(f5(A, 1, C, D, E)) :|: A >= 2
3.91/1.89	f4(A, B, C, D, E) -> Com_1(f5(A, 0, C, D, E)) :|: 1 >= A
3.91/1.89	f30(A, B, C, D, E) -> Com_1(f4(2, B, 2, F, E)) :|: TRUE
3.91/1.89	f5(A, B, C, D, E) -> Com_1(f4(A - 1, B, C, F, E)) :|: 0 >= F && F >= 1
3.91/1.89	f5(A, B, C, D, E) -> Com_1(f4(A + 1, B, C, F, E)) :|: F >= 1
3.91/1.89	f5(A, B, C, D, E) -> Com_1(f3(A, B, C, D, 0)) :|: 0 >= B
3.91/1.89	
3.91/1.89	The start-symbols are:[f30_5]
3.91/1.89	
3.91/1.89	
3.91/1.89	----------------------------------------
3.91/1.89	
3.91/1.89	(1) Loat Proof (FINISHED)
3.91/1.89	
3.91/1.89	
3.91/1.89	### Pre-processing the ITS problem ###
3.91/1.89	
3.91/1.89	
3.91/1.89	
3.91/1.89	Initial linear ITS problem
3.91/1.89	
3.91/1.89	   Start location: f30
3.91/1.89	
3.91/1.89	      0: f4 -> f5 : B'=1, [ A>=2 ], cost: 1
3.91/1.89	
3.91/1.89	      1: f4 -> f5 : B'=0, [ 1>=A ], cost: 1
3.91/1.89	
3.91/1.89	      2: f30 -> f4 : A'=2, C'=2, D'=free, [], cost: 1
3.91/1.89	
3.91/1.89	      3: f5 -> f4 : A'=-1+A, D'=free_1, [ 0>=free_1 && free_1>=1 ], cost: 1
3.91/1.89	
3.91/1.89	      4: f5 -> f4 : A'=1+A, D'=free_2, [ free_2>=1 ], cost: 1
3.91/1.89	
3.91/1.89	      5: f5 -> f3 : E'=0, [ 0>=B ], cost: 1
3.91/1.89	
3.91/1.89	
3.91/1.89	
3.91/1.89	Removed unreachable and leaf rules:
3.91/1.89	
3.91/1.89	   Start location: f30
3.91/1.89	
3.91/1.89	      0: f4 -> f5 : B'=1, [ A>=2 ], cost: 1
3.91/1.89	
3.91/1.89	      1: f4 -> f5 : B'=0, [ 1>=A ], cost: 1
3.91/1.89	
3.91/1.89	      2: f30 -> f4 : A'=2, C'=2, D'=free, [], cost: 1
3.91/1.89	
3.91/1.89	      3: f5 -> f4 : A'=-1+A, D'=free_1, [ 0>=free_1 && free_1>=1 ], cost: 1
3.91/1.89	
3.91/1.89	      4: f5 -> f4 : A'=1+A, D'=free_2, [ free_2>=1 ], cost: 1
3.91/1.89	
3.91/1.89	
3.91/1.89	
3.91/1.89	Removed rules with unsatisfiable guard:
3.91/1.89	
3.91/1.89	   Start location: f30
3.91/1.89	
3.91/1.89	      0: f4 -> f5 : B'=1, [ A>=2 ], cost: 1
3.91/1.89	
3.91/1.89	      1: f4 -> f5 : B'=0, [ 1>=A ], cost: 1
3.91/1.89	
3.91/1.89	      2: f30 -> f4 : A'=2, C'=2, D'=free, [], cost: 1
3.91/1.89	
3.91/1.89	      4: f5 -> f4 : A'=1+A, D'=free_2, [ free_2>=1 ], cost: 1
3.91/1.89	
3.91/1.89	
3.91/1.89	
3.91/1.89	### Simplification by acceleration and chaining ###
3.91/1.89	
3.91/1.89	
3.91/1.89	
3.91/1.89	Eliminated locations (on tree-shaped paths):
3.91/1.89	
3.91/1.89	   Start location: f30
3.91/1.89	
3.91/1.89	      6: f4 -> f4 : A'=1+A, B'=1, D'=free_2, [ A>=2 && free_2>=1 ], cost: 2
3.91/1.89	
3.91/1.89	      7: f4 -> f4 : A'=1+A, B'=0, D'=free_2, [ 1>=A && free_2>=1 ], cost: 2
3.91/1.89	
3.91/1.89	      2: f30 -> f4 : A'=2, C'=2, D'=free, [], cost: 1
3.91/1.89	
3.91/1.89	
3.91/1.89	
3.91/1.89	Accelerating simple loops of location 0.
3.91/1.89	
3.91/1.89	   Accelerating the following rules:
3.91/1.89	
3.91/1.89	      6: f4 -> f4 : A'=1+A, B'=1, D'=free_2, [ A>=2 && free_2>=1 ], cost: 2
3.91/1.89	
3.91/1.89	      7: f4 -> f4 : A'=1+A, B'=0, D'=free_2, [ 1>=A && free_2>=1 ], cost: 2
3.91/1.89	
3.91/1.89	
3.91/1.89	
3.91/1.89	   Accelerated rule 6 with NONTERM, yielding the new rule 8.
3.91/1.89	
3.91/1.89	   Accelerated rule 7 with metering function 2-A, yielding the new rule 9.
3.91/1.89	
3.91/1.89	   Removing the simple loops: 6 7.
3.91/1.89	
3.91/1.89	
3.91/1.89	
3.91/1.89	Accelerated all simple loops using metering functions (where possible):
3.91/1.89	
3.91/1.89	   Start location: f30
3.91/1.89	
3.91/1.89	      8: f4 -> [4] : [ A>=2 && free_2>=1 ], cost: INF
3.91/1.89	
3.91/1.89	      9: f4 -> f4 : A'=2, B'=0, D'=free_2, [ 1>=A && free_2>=1 ], cost: 4-2*A
3.91/1.89	
3.91/1.89	      2: f30 -> f4 : A'=2, C'=2, D'=free, [], cost: 1
3.91/1.89	
3.91/1.89	
3.91/1.89	
3.91/1.89	Chained accelerated rules (with incoming rules):
3.91/1.89	
3.91/1.89	   Start location: f30
3.91/1.89	
3.91/1.89	      2: f30 -> f4 : A'=2, C'=2, D'=free, [], cost: 1
3.91/1.89	
3.91/1.89	     10: f30 -> [4] : A'=2, C'=2, D'=free, [], cost: INF
3.91/1.89	
3.91/1.89	
3.91/1.89	
3.91/1.89	Removed unreachable locations (and leaf rules with constant cost):
3.91/1.89	
3.91/1.89	   Start location: f30
3.91/1.89	
3.91/1.89	     10: f30 -> [4] : A'=2, C'=2, D'=free, [], cost: INF
3.91/1.89	
3.91/1.89	
3.91/1.89	
3.91/1.89	### Computing asymptotic complexity ###
3.91/1.89	
3.91/1.89	
3.91/1.89	
3.91/1.89	Fully simplified ITS problem
3.91/1.89	
3.91/1.89	   Start location: f30
3.91/1.89	
3.91/1.89	     10: f30 -> [4] : A'=2, C'=2, D'=free, [], cost: INF
3.91/1.89	
3.91/1.89	
3.91/1.89	
3.91/1.89	Computing asymptotic complexity for rule 10
3.91/1.89	
3.91/1.89	   Resulting cost INF has complexity: Nonterm
3.91/1.89	
3.91/1.89	
3.91/1.89	
3.91/1.89	Found new complexity Nonterm.
3.91/1.89	
3.91/1.89	
3.91/1.89	
3.91/1.89	Obtained the following overall complexity (w.r.t. the length of the input n):
3.91/1.89	
3.91/1.89	   Complexity:  Nonterm
3.91/1.89	
3.91/1.89	   Cpx degree:  Nonterm
3.91/1.89	
3.91/1.89	   Solved cost: INF
3.91/1.89	
3.91/1.89	   Rule cost:   INF
3.91/1.89	
3.91/1.89	   Rule guard:  []
3.91/1.89	
3.91/1.89	
3.91/1.89	
3.91/1.89	NO
3.91/1.89	
3.91/1.89	
3.91/1.89	----------------------------------------
3.91/1.89	
3.91/1.89	(2)
3.91/1.89	BOUNDS(INF, INF)
4.18/1.91	EOF