4.27/2.03	WORST_CASE(Omega(n^1), O(n^1))
4.27/2.04	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
4.27/2.04	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.27/2.04	
4.27/2.04	
4.27/2.04	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
4.27/2.04	
4.27/2.04	(0) CpxIntTrs
4.27/2.04	(1) Koat Proof [FINISHED, 22 ms]
4.27/2.04	(2) BOUNDS(1, n^1)
4.27/2.04	(3) Loat Proof [FINISHED, 324 ms]
4.27/2.04	(4) BOUNDS(n^1, INF)
4.27/2.04	
4.27/2.04	
4.27/2.04	----------------------------------------
4.27/2.04	
4.27/2.04	(0)
4.27/2.04	Obligation:
4.27/2.04	Complexity Int TRS consisting of the following rules:
4.27/2.04	eval_ndecr_start(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_bb0_in(v_0, v_i_0, v_n)) :|: TRUE
4.27/2.04	eval_ndecr_bb0_in(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_0(v_0, v_i_0, v_n)) :|: TRUE
4.27/2.04	eval_ndecr_0(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_1(v_0, v_i_0, v_n)) :|: TRUE
4.27/2.04	eval_ndecr_1(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_2(v_n - 1, v_i_0, v_n)) :|: TRUE
4.27/2.04	eval_ndecr_2(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_3(v_0, v_i_0, v_n)) :|: TRUE
4.27/2.04	eval_ndecr_3(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_4(v_0, v_i_0, v_n)) :|: TRUE
4.27/2.04	eval_ndecr_4(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_bb1_in(v_0, v_0, v_n)) :|: TRUE
4.27/2.04	eval_ndecr_bb1_in(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_bb2_in(v_0, v_i_0, v_n)) :|: v_i_0 > 1
4.27/2.04	eval_ndecr_bb1_in(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_bb3_in(v_0, v_i_0, v_n)) :|: v_i_0 <= 1
4.27/2.04	eval_ndecr_bb2_in(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_bb1_in(v_0, v_i_0 - 1, v_n)) :|: TRUE
4.27/2.04	eval_ndecr_bb3_in(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_stop(v_0, v_i_0, v_n)) :|: TRUE
4.27/2.04	
4.27/2.04	The start-symbols are:[eval_ndecr_start_3]
4.27/2.04	
4.27/2.04	
4.27/2.04	----------------------------------------
4.27/2.04	
4.27/2.04	(1) Koat Proof (FINISHED)
4.27/2.04	YES(?, 2*ar_1 + 11)
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	Initial complexity problem:
4.27/2.04	
4.27/2.04	1:	T:
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)    evalndecrstart(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb0in(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)    evalndecrbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndecr0(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)    evalndecr0(ar_0, ar_1, ar_2) -> Com_1(evalndecr1(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)    evalndecr1(ar_0, ar_1, ar_2) -> Com_1(evalndecr2(ar_1 - 1, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)    evalndecr2(ar_0, ar_1, ar_2) -> Com_1(evalndecr3(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)    evalndecr3(ar_0, ar_1, ar_2) -> Com_1(evalndecr4(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)    evalndecr4(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb1in(ar_0, ar_1, ar_0))
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)    evalndecrbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)    evalndecrbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb3in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)    evalndecrbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb1in(ar_0, ar_1, ar_2 - 1))
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)    evalndecrbb3in(ar_0, ar_1, ar_2) -> Com_1(evalndecrstop(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndecrstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.27/2.04	
4.27/2.04		start location:	koat_start
4.27/2.04	
4.27/2.04		leaf cost:	0
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	Repeatedly propagating knowledge in problem 1 produces the following problem:
4.27/2.04	
4.27/2.04	2:	T:
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)    evalndecrstart(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb0in(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)    evalndecrbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndecr0(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)    evalndecr0(ar_0, ar_1, ar_2) -> Com_1(evalndecr1(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)    evalndecr1(ar_0, ar_1, ar_2) -> Com_1(evalndecr2(ar_1 - 1, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)    evalndecr2(ar_0, ar_1, ar_2) -> Com_1(evalndecr3(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)    evalndecr3(ar_0, ar_1, ar_2) -> Com_1(evalndecr4(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)    evalndecr4(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb1in(ar_0, ar_1, ar_0))
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)    evalndecrbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)    evalndecrbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb3in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)    evalndecrbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb1in(ar_0, ar_1, ar_2 - 1))
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)    evalndecrbb3in(ar_0, ar_1, ar_2) -> Com_1(evalndecrstop(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndecrstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.27/2.04	
4.27/2.04		start location:	koat_start
4.27/2.04	
4.27/2.04		leaf cost:	0
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	A polynomial rank function with
4.27/2.04	
4.27/2.04		Pol(evalndecrstart) = 2
4.27/2.04	
4.27/2.04		Pol(evalndecrbb0in) = 2
4.27/2.04	
4.27/2.04		Pol(evalndecr0) = 2
4.27/2.04	
4.27/2.04		Pol(evalndecr1) = 2
4.27/2.04	
4.27/2.04		Pol(evalndecr2) = 2
4.27/2.04	
4.27/2.04		Pol(evalndecr3) = 2
4.27/2.04	
4.27/2.04		Pol(evalndecr4) = 2
4.27/2.04	
4.27/2.04		Pol(evalndecrbb1in) = 2
4.27/2.04	
4.27/2.04		Pol(evalndecrbb2in) = 2
4.27/2.04	
4.27/2.04		Pol(evalndecrbb3in) = 1
4.27/2.04	
4.27/2.04		Pol(evalndecrstop) = 0
4.27/2.04	
4.27/2.04		Pol(koat_start) = 2
4.27/2.04	
4.27/2.04	orients all transitions weakly and the transitions
4.27/2.04	
4.27/2.04		evalndecrbb3in(ar_0, ar_1, ar_2) -> Com_1(evalndecrstop(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04		evalndecrbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb3in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]
4.27/2.04	
4.27/2.04	strictly and produces the following problem:
4.27/2.04	
4.27/2.04	3:	T:
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)    evalndecrstart(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb0in(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)    evalndecrbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndecr0(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)    evalndecr0(ar_0, ar_1, ar_2) -> Com_1(evalndecr1(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)    evalndecr1(ar_0, ar_1, ar_2) -> Com_1(evalndecr2(ar_1 - 1, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)    evalndecr2(ar_0, ar_1, ar_2) -> Com_1(evalndecr3(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)    evalndecr3(ar_0, ar_1, ar_2) -> Com_1(evalndecr4(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)    evalndecr4(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb1in(ar_0, ar_1, ar_0))
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)    evalndecrbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]
4.27/2.04	
4.27/2.04			(Comp: 2, Cost: 1)    evalndecrbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb3in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)    evalndecrbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb1in(ar_0, ar_1, ar_2 - 1))
4.27/2.04	
4.27/2.04			(Comp: 2, Cost: 1)    evalndecrbb3in(ar_0, ar_1, ar_2) -> Com_1(evalndecrstop(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndecrstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.27/2.04	
4.27/2.04		start location:	koat_start
4.27/2.04	
4.27/2.04		leaf cost:	0
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	A polynomial rank function with
4.27/2.04	
4.27/2.04		Pol(evalndecrstart) = V_2
4.27/2.04	
4.27/2.04		Pol(evalndecrbb0in) = V_2
4.27/2.04	
4.27/2.04		Pol(evalndecr0) = V_2
4.27/2.04	
4.27/2.04		Pol(evalndecr1) = V_2
4.27/2.04	
4.27/2.04		Pol(evalndecr2) = V_1
4.27/2.04	
4.27/2.04		Pol(evalndecr3) = V_1
4.27/2.04	
4.27/2.04		Pol(evalndecr4) = V_1
4.27/2.04	
4.27/2.04		Pol(evalndecrbb1in) = V_3
4.27/2.04	
4.27/2.04		Pol(evalndecrbb2in) = V_3 - 1
4.27/2.04	
4.27/2.04		Pol(evalndecrbb3in) = V_3
4.27/2.04	
4.27/2.04		Pol(evalndecrstop) = V_3
4.27/2.04	
4.27/2.04		Pol(koat_start) = V_2
4.27/2.04	
4.27/2.04	orients all transitions weakly and the transition
4.27/2.04	
4.27/2.04		evalndecrbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]
4.27/2.04	
4.27/2.04	strictly and produces the following problem:
4.27/2.04	
4.27/2.04	4:	T:
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)       evalndecrstart(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb0in(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)       evalndecrbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndecr0(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)       evalndecr0(ar_0, ar_1, ar_2) -> Com_1(evalndecr1(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)       evalndecr1(ar_0, ar_1, ar_2) -> Com_1(evalndecr2(ar_1 - 1, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)       evalndecr2(ar_0, ar_1, ar_2) -> Com_1(evalndecr3(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)       evalndecr3(ar_0, ar_1, ar_2) -> Com_1(evalndecr4(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)       evalndecr4(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb1in(ar_0, ar_1, ar_0))
4.27/2.04	
4.27/2.04			(Comp: ar_1, Cost: 1)    evalndecrbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]
4.27/2.04	
4.27/2.04			(Comp: 2, Cost: 1)       evalndecrbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb3in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]
4.27/2.04	
4.27/2.04			(Comp: ?, Cost: 1)       evalndecrbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb1in(ar_0, ar_1, ar_2 - 1))
4.27/2.04	
4.27/2.04			(Comp: 2, Cost: 1)       evalndecrbb3in(ar_0, ar_1, ar_2) -> Com_1(evalndecrstop(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndecrstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.27/2.04	
4.27/2.04		start location:	koat_start
4.27/2.04	
4.27/2.04		leaf cost:	0
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	Repeatedly propagating knowledge in problem 4 produces the following problem:
4.27/2.04	
4.27/2.04	5:	T:
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)       evalndecrstart(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb0in(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)       evalndecrbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndecr0(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)       evalndecr0(ar_0, ar_1, ar_2) -> Com_1(evalndecr1(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)       evalndecr1(ar_0, ar_1, ar_2) -> Com_1(evalndecr2(ar_1 - 1, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)       evalndecr2(ar_0, ar_1, ar_2) -> Com_1(evalndecr3(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)       evalndecr3(ar_0, ar_1, ar_2) -> Com_1(evalndecr4(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 1)       evalndecr4(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb1in(ar_0, ar_1, ar_0))
4.27/2.04	
4.27/2.04			(Comp: ar_1, Cost: 1)    evalndecrbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]
4.27/2.04	
4.27/2.04			(Comp: 2, Cost: 1)       evalndecrbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb3in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ]
4.27/2.04	
4.27/2.04			(Comp: ar_1, Cost: 1)    evalndecrbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb1in(ar_0, ar_1, ar_2 - 1))
4.27/2.04	
4.27/2.04			(Comp: 2, Cost: 1)       evalndecrbb3in(ar_0, ar_1, ar_2) -> Com_1(evalndecrstop(ar_0, ar_1, ar_2))
4.27/2.04	
4.27/2.04			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndecrstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.27/2.04	
4.27/2.04		start location:	koat_start
4.27/2.04	
4.27/2.04		leaf cost:	0
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	Complexity upper bound 2*ar_1 + 11
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	Time: 0.079 sec (SMT: 0.069 sec)
4.27/2.04	
4.27/2.04	
4.27/2.04	----------------------------------------
4.27/2.04	
4.27/2.04	(2)
4.27/2.04	BOUNDS(1, n^1)
4.27/2.04	
4.27/2.04	----------------------------------------
4.27/2.04	
4.27/2.04	(3) Loat Proof (FINISHED)
4.27/2.04	
4.27/2.04	
4.27/2.04	### Pre-processing the ITS problem ###
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	Initial linear ITS problem
4.27/2.04	
4.27/2.04	   Start location: evalndecrstart
4.27/2.04	
4.27/2.04	      0: evalndecrstart -> evalndecrbb0in : [], cost: 1
4.27/2.04	
4.27/2.04	      1: evalndecrbb0in -> evalndecr0 : [], cost: 1
4.27/2.04	
4.27/2.04	      2: evalndecr0 -> evalndecr1 : [], cost: 1
4.27/2.04	
4.27/2.04	      3: evalndecr1 -> evalndecr2 : A'=-1+B, [], cost: 1
4.27/2.04	
4.27/2.04	      4: evalndecr2 -> evalndecr3 : [], cost: 1
4.27/2.04	
4.27/2.04	      5: evalndecr3 -> evalndecr4 : [], cost: 1
4.27/2.04	
4.27/2.04	      6: evalndecr4 -> evalndecrbb1in : C'=A, [], cost: 1
4.27/2.04	
4.27/2.04	      7: evalndecrbb1in -> evalndecrbb2in : [ C>=2 ], cost: 1
4.27/2.04	
4.27/2.04	      8: evalndecrbb1in -> evalndecrbb3in : [ 1>=C ], cost: 1
4.27/2.04	
4.27/2.04	      9: evalndecrbb2in -> evalndecrbb1in : C'=-1+C, [], cost: 1
4.27/2.04	
4.27/2.04	     10: evalndecrbb3in -> evalndecrstop : [], cost: 1
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	Removed unreachable and leaf rules:
4.27/2.04	
4.27/2.04	   Start location: evalndecrstart
4.27/2.04	
4.27/2.04	      0: evalndecrstart -> evalndecrbb0in : [], cost: 1
4.27/2.04	
4.27/2.04	      1: evalndecrbb0in -> evalndecr0 : [], cost: 1
4.27/2.04	
4.27/2.04	      2: evalndecr0 -> evalndecr1 : [], cost: 1
4.27/2.04	
4.27/2.04	      3: evalndecr1 -> evalndecr2 : A'=-1+B, [], cost: 1
4.27/2.04	
4.27/2.04	      4: evalndecr2 -> evalndecr3 : [], cost: 1
4.27/2.04	
4.27/2.04	      5: evalndecr3 -> evalndecr4 : [], cost: 1
4.27/2.04	
4.27/2.04	      6: evalndecr4 -> evalndecrbb1in : C'=A, [], cost: 1
4.27/2.04	
4.27/2.04	      7: evalndecrbb1in -> evalndecrbb2in : [ C>=2 ], cost: 1
4.27/2.04	
4.27/2.04	      9: evalndecrbb2in -> evalndecrbb1in : C'=-1+C, [], cost: 1
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	### Simplification by acceleration and chaining ###
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	Eliminated locations (on linear paths):
4.27/2.04	
4.27/2.04	   Start location: evalndecrstart
4.27/2.04	
4.27/2.04	     16: evalndecrstart -> evalndecrbb1in : A'=-1+B, C'=-1+B, [], cost: 7
4.27/2.04	
4.27/2.04	     17: evalndecrbb1in -> evalndecrbb1in : C'=-1+C, [ C>=2 ], cost: 2
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	Accelerating simple loops of location 7.
4.27/2.04	
4.27/2.04	   Accelerating the following rules:
4.27/2.04	
4.27/2.04	     17: evalndecrbb1in -> evalndecrbb1in : C'=-1+C, [ C>=2 ], cost: 2
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	   Accelerated rule 17 with metering function -1+C, yielding the new rule 18.
4.27/2.04	
4.27/2.04	   Removing the simple loops: 17.
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	Accelerated all simple loops using metering functions (where possible):
4.27/2.04	
4.27/2.04	   Start location: evalndecrstart
4.27/2.04	
4.27/2.04	     16: evalndecrstart -> evalndecrbb1in : A'=-1+B, C'=-1+B, [], cost: 7
4.27/2.04	
4.27/2.04	     18: evalndecrbb1in -> evalndecrbb1in : C'=1, [ C>=2 ], cost: -2+2*C
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	Chained accelerated rules (with incoming rules):
4.27/2.04	
4.27/2.04	   Start location: evalndecrstart
4.27/2.04	
4.27/2.04	     16: evalndecrstart -> evalndecrbb1in : A'=-1+B, C'=-1+B, [], cost: 7
4.27/2.04	
4.27/2.04	     19: evalndecrstart -> evalndecrbb1in : A'=-1+B, C'=1, [ -1+B>=2 ], cost: 3+2*B
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	Removed unreachable locations (and leaf rules with constant cost):
4.27/2.04	
4.27/2.04	   Start location: evalndecrstart
4.27/2.04	
4.27/2.04	     19: evalndecrstart -> evalndecrbb1in : A'=-1+B, C'=1, [ -1+B>=2 ], cost: 3+2*B
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	### Computing asymptotic complexity ###
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	Fully simplified ITS problem
4.27/2.04	
4.27/2.04	   Start location: evalndecrstart
4.27/2.04	
4.27/2.04	     19: evalndecrstart -> evalndecrbb1in : A'=-1+B, C'=1, [ -1+B>=2 ], cost: 3+2*B
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	Computing asymptotic complexity for rule 19
4.27/2.04	
4.27/2.04	   Solved the limit problem by the following transformations:
4.27/2.04	
4.27/2.04	      Created initial limit problem:
4.27/2.04	
4.27/2.04	      -2+B (+/+!), 3+2*B (+) [not solved]
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	      removing all constraints (solved by SMT)
4.27/2.04	
4.27/2.04	      resulting limit problem: [solved]
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	      applying transformation rule (C) using substitution {B==n}
4.27/2.04	
4.27/2.04	      resulting limit problem:
4.27/2.04	
4.27/2.04	      [solved]
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	   Solution:
4.27/2.04	
4.27/2.04	      B / n
4.27/2.04	
4.27/2.04	   Resulting cost 3+2*n has complexity: Poly(n^1)
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	Found new complexity Poly(n^1).
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	Obtained the following overall complexity (w.r.t. the length of the input n):
4.27/2.04	
4.27/2.04	   Complexity:  Poly(n^1)
4.27/2.04	
4.27/2.04	   Cpx degree:  1
4.27/2.04	
4.27/2.04	   Solved cost: 3+2*n
4.27/2.04	
4.27/2.04	   Rule cost:   3+2*B
4.27/2.04	
4.27/2.04	   Rule guard:  [ -1+B>=2 ]
4.27/2.04	
4.27/2.04	
4.27/2.04	
4.27/2.04	WORST_CASE(Omega(n^1),?)
4.27/2.04	
4.27/2.04	
4.27/2.04	----------------------------------------
4.27/2.04	
4.27/2.04	(4)
4.27/2.04	BOUNDS(n^1, INF)
4.27/2.06	EOF