3.71/1.92	WORST_CASE(NON_POLY, ?)
3.71/1.92	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.71/1.92	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.71/1.92	
3.71/1.92	
3.71/1.92	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.71/1.92	
3.71/1.92	(0) CpxIntTrs
3.71/1.92	(1) Loat Proof [FINISHED, 222 ms]
3.71/1.92	(2) BOUNDS(INF, INF)
3.71/1.92	
3.71/1.92	
3.71/1.92	----------------------------------------
3.71/1.92	
3.71/1.92	(0)
3.71/1.92	Obligation:
3.71/1.92	Complexity Int TRS consisting of the following rules:
3.71/1.92	f0(A, B, C, D) -> Com_1(f6(B, B, D, D)) :|: TRUE
3.71/1.92	f6(A, B, C, D) -> Com_1(f6(A - 1, B, C - 1, D)) :|: 0 >= A + 1
3.71/1.92	f6(A, B, C, D) -> Com_1(f6(A - 1, B, C - 1, D)) :|: A >= 1
3.71/1.92	f6(A, B, C, D) -> Com_1(f14(0, B, C, D)) :|: D >= B + 1 && A >= 0 && A <= 0
3.71/1.92	f6(A, B, C, D) -> Com_1(f14(0, B, C, D)) :|: B >= 1 + D && A >= 0 && A <= 0
3.71/1.92	f6(A, B, C, D) -> Com_1(f14(0, B, C, B)) :|: A >= 0 && A <= 0 && B >= D && B <= D
3.71/1.92	
3.71/1.92	The start-symbols are:[f0_4]
3.71/1.92	
3.71/1.92	
3.71/1.92	----------------------------------------
3.71/1.92	
3.71/1.92	(1) Loat Proof (FINISHED)
3.71/1.92	
3.71/1.92	
3.71/1.92	### Pre-processing the ITS problem ###
3.71/1.92	
3.71/1.92	
3.71/1.92	
3.71/1.92	Initial linear ITS problem
3.71/1.92	
3.71/1.92	   Start location: f0
3.71/1.93	
3.71/1.93	      0: f0 -> f6 : A'=B, C'=D, [], cost: 1
3.71/1.93	
3.71/1.93	      1: f6 -> f6 : A'=-1+A, C'=-1+C, [ 0>=1+A ], cost: 1
3.71/1.93	
3.71/1.93	      2: f6 -> f6 : A'=-1+A, C'=-1+C, [ A>=1 ], cost: 1
3.71/1.93	
3.71/1.93	      3: f6 -> f14 : A'=0, [ D>=1+B && A==0 ], cost: 1
3.71/1.93	
3.71/1.93	      4: f6 -> f14 : A'=0, [ B>=1+D && A==0 ], cost: 1
3.71/1.93	
3.71/1.93	      5: f6 -> f14 : A'=0, D'=B, [ A==0 && B==D ], cost: 1
3.71/1.93	
3.71/1.93	
3.71/1.93	
3.71/1.93	Removed unreachable and leaf rules:
3.71/1.93	
3.71/1.93	   Start location: f0
3.71/1.93	
3.71/1.93	      0: f0 -> f6 : A'=B, C'=D, [], cost: 1
3.71/1.93	
3.71/1.93	      1: f6 -> f6 : A'=-1+A, C'=-1+C, [ 0>=1+A ], cost: 1
3.71/1.93	
3.71/1.93	      2: f6 -> f6 : A'=-1+A, C'=-1+C, [ A>=1 ], cost: 1
3.71/1.93	
3.71/1.93	
3.71/1.93	
3.71/1.93	### Simplification by acceleration and chaining ###
3.71/1.93	
3.71/1.93	
3.71/1.93	
3.71/1.93	Accelerating simple loops of location 1.
3.71/1.93	
3.71/1.93	   Accelerating the following rules:
3.71/1.93	
3.71/1.93	      1: f6 -> f6 : A'=-1+A, C'=-1+C, [ 0>=1+A ], cost: 1
3.71/1.93	
3.71/1.93	      2: f6 -> f6 : A'=-1+A, C'=-1+C, [ A>=1 ], cost: 1
3.71/1.93	
3.71/1.93	
3.71/1.93	
3.71/1.93	   Accelerated rule 1 with NONTERM, yielding the new rule 6.
3.71/1.93	
3.71/1.93	   Accelerated rule 2 with metering function A, yielding the new rule 7.
3.71/1.93	
3.71/1.93	   Removing the simple loops: 1 2.
3.71/1.93	
3.71/1.93	
3.71/1.93	
3.71/1.93	Accelerated all simple loops using metering functions (where possible):
3.71/1.93	
3.71/1.93	   Start location: f0
3.71/1.93	
3.71/1.93	      0: f0 -> f6 : A'=B, C'=D, [], cost: 1
3.71/1.93	
3.71/1.93	      6: f6 -> [3] : [ 0>=1+A ], cost: INF
3.71/1.93	
3.71/1.93	      7: f6 -> f6 : A'=0, C'=C-A, [ A>=1 ], cost: A
3.71/1.93	
3.71/1.93	
3.71/1.93	
3.71/1.93	Chained accelerated rules (with incoming rules):
3.71/1.93	
3.71/1.93	   Start location: f0
3.71/1.93	
3.71/1.93	      0: f0 -> f6 : A'=B, C'=D, [], cost: 1
3.71/1.93	
3.71/1.93	      8: f0 -> [3] : A'=B, C'=D, [ 0>=1+B ], cost: INF
3.71/1.93	
3.71/1.93	      9: f0 -> f6 : A'=0, C'=D-B, [ B>=1 ], cost: 1+B
3.71/1.93	
3.71/1.93	
3.71/1.93	
3.71/1.93	Removed unreachable locations (and leaf rules with constant cost):
3.71/1.93	
3.71/1.93	   Start location: f0
3.71/1.93	
3.71/1.93	      8: f0 -> [3] : A'=B, C'=D, [ 0>=1+B ], cost: INF
3.71/1.93	
3.71/1.93	      9: f0 -> f6 : A'=0, C'=D-B, [ B>=1 ], cost: 1+B
3.71/1.93	
3.71/1.93	
3.71/1.93	
3.71/1.93	### Computing asymptotic complexity ###
3.71/1.93	
3.71/1.93	
3.71/1.93	
3.71/1.93	Fully simplified ITS problem
3.71/1.93	
3.71/1.93	   Start location: f0
3.71/1.93	
3.71/1.93	      8: f0 -> [3] : A'=B, C'=D, [ 0>=1+B ], cost: INF
3.71/1.93	
3.71/1.93	      9: f0 -> f6 : A'=0, C'=D-B, [ B>=1 ], cost: 1+B
3.71/1.93	
3.71/1.93	
3.71/1.93	
3.71/1.93	Computing asymptotic complexity for rule 8
3.71/1.93	
3.71/1.93	   Resulting cost INF has complexity: Nonterm
3.71/1.93	
3.71/1.93	
3.71/1.93	
3.71/1.93	Found new complexity Nonterm.
3.71/1.93	
3.71/1.93	
3.71/1.93	
3.71/1.93	Obtained the following overall complexity (w.r.t. the length of the input n):
3.71/1.93	
3.71/1.93	   Complexity:  Nonterm
3.71/1.93	
3.71/1.93	   Cpx degree:  Nonterm
3.71/1.93	
3.71/1.93	   Solved cost: INF
3.71/1.93	
3.71/1.93	   Rule cost:   INF
3.71/1.93	
3.71/1.93	   Rule guard:  [ 0>=1+B ]
3.71/1.93	
3.71/1.93	
3.71/1.93	
3.71/1.93	NO
3.71/1.93	
3.71/1.93	
3.71/1.93	----------------------------------------
3.71/1.93	
3.71/1.93	(2)
3.71/1.93	BOUNDS(INF, INF)
3.71/1.95	EOF