4.43/2.14	WORST_CASE(Omega(n^1), O(n^1))
4.43/2.15	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.43/2.15	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.43/2.15	
4.43/2.15	
4.43/2.15	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
4.43/2.15	
4.43/2.15	(0) CpxIntTrs
4.43/2.15	(1) Koat Proof [FINISHED, 27 ms]
4.43/2.15	(2) BOUNDS(1, n^1)
4.43/2.15	(3) Loat Proof [FINISHED, 399 ms]
4.43/2.15	(4) BOUNDS(n^1, INF)
4.43/2.15	
4.43/2.15	
4.43/2.15	----------------------------------------
4.43/2.15	
4.43/2.15	(0)
4.43/2.15	Obligation:
4.43/2.15	Complexity Int TRS consisting of the following rules:
4.43/2.15	eval_easy2_start(v__0, v_z) -> Com_1(eval_easy2_bb0_in(v__0, v_z)) :|: TRUE
4.43/2.15	eval_easy2_bb0_in(v__0, v_z) -> Com_1(eval_easy2_0(v__0, v_z)) :|: TRUE
4.43/2.15	eval_easy2_0(v__0, v_z) -> Com_1(eval_easy2_1(v__0, v_z)) :|: TRUE
4.43/2.15	eval_easy2_1(v__0, v_z) -> Com_1(eval_easy2_2(v__0, v_z)) :|: TRUE
4.43/2.15	eval_easy2_2(v__0, v_z) -> Com_1(eval_easy2_3(v__0, v_z)) :|: TRUE
4.43/2.15	eval_easy2_3(v__0, v_z) -> Com_1(eval_easy2_4(v__0, v_z)) :|: TRUE
4.43/2.15	eval_easy2_4(v__0, v_z) -> Com_1(eval_easy2_5(v__0, v_z)) :|: TRUE
4.43/2.15	eval_easy2_5(v__0, v_z) -> Com_1(eval_easy2_6(v__0, v_z)) :|: TRUE
4.43/2.15	eval_easy2_6(v__0, v_z) -> Com_1(eval_easy2_bb1_in(v_z, v_z)) :|: TRUE
4.43/2.15	eval_easy2_bb1_in(v__0, v_z) -> Com_1(eval_easy2_bb2_in(v__0, v_z)) :|: v__0 > 0
4.43/2.15	eval_easy2_bb1_in(v__0, v_z) -> Com_1(eval_easy2_bb3_in(v__0, v_z)) :|: v__0 <= 0
4.43/2.15	eval_easy2_bb2_in(v__0, v_z) -> Com_1(eval_easy2_bb1_in(v__0 - 1, v_z)) :|: TRUE
4.43/2.15	eval_easy2_bb3_in(v__0, v_z) -> Com_1(eval_easy2_stop(v__0, v_z)) :|: TRUE
4.43/2.15	
4.43/2.15	The start-symbols are:[eval_easy2_start_2]
4.43/2.15	
4.43/2.15	
4.43/2.15	----------------------------------------
4.43/2.15	
4.43/2.15	(1) Koat Proof (FINISHED)
4.43/2.15	YES(?, 2*ar_1 + 15)
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	Initial complexity problem:
4.43/2.15	
4.43/2.15	1:	T:
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy2start(ar_0, ar_1) -> Com_1(evaleasy2bb0in(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy2bb0in(ar_0, ar_1) -> Com_1(evaleasy20(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy20(ar_0, ar_1) -> Com_1(evaleasy21(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy21(ar_0, ar_1) -> Com_1(evaleasy22(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy22(ar_0, ar_1) -> Com_1(evaleasy23(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy23(ar_0, ar_1) -> Com_1(evaleasy24(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy24(ar_0, ar_1) -> Com_1(evaleasy25(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy25(ar_0, ar_1) -> Com_1(evaleasy26(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy26(ar_0, ar_1) -> Com_1(evaleasy2bb1in(ar_1, ar_1))
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy2bb1in(ar_0, ar_1) -> Com_1(evaleasy2bb2in(ar_0, ar_1)) [ ar_0 >= 1 ]
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy2bb1in(ar_0, ar_1) -> Com_1(evaleasy2bb3in(ar_0, ar_1)) [ 0 >= ar_0 ]
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy2bb2in(ar_0, ar_1) -> Com_1(evaleasy2bb1in(ar_0 - 1, ar_1))
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy2bb3in(ar_0, ar_1) -> Com_1(evaleasy2stop(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evaleasy2start(ar_0, ar_1)) [ 0 <= 0 ]
4.43/2.15	
4.43/2.15		start location:	koat_start
4.43/2.15	
4.43/2.15		leaf cost:	0
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	Repeatedly propagating knowledge in problem 1 produces the following problem:
4.43/2.15	
4.43/2.15	2:	T:
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy2start(ar_0, ar_1) -> Com_1(evaleasy2bb0in(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy2bb0in(ar_0, ar_1) -> Com_1(evaleasy20(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy20(ar_0, ar_1) -> Com_1(evaleasy21(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy21(ar_0, ar_1) -> Com_1(evaleasy22(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy22(ar_0, ar_1) -> Com_1(evaleasy23(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy23(ar_0, ar_1) -> Com_1(evaleasy24(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy24(ar_0, ar_1) -> Com_1(evaleasy25(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy25(ar_0, ar_1) -> Com_1(evaleasy26(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy26(ar_0, ar_1) -> Com_1(evaleasy2bb1in(ar_1, ar_1))
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy2bb1in(ar_0, ar_1) -> Com_1(evaleasy2bb2in(ar_0, ar_1)) [ ar_0 >= 1 ]
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy2bb1in(ar_0, ar_1) -> Com_1(evaleasy2bb3in(ar_0, ar_1)) [ 0 >= ar_0 ]
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy2bb2in(ar_0, ar_1) -> Com_1(evaleasy2bb1in(ar_0 - 1, ar_1))
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy2bb3in(ar_0, ar_1) -> Com_1(evaleasy2stop(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evaleasy2start(ar_0, ar_1)) [ 0 <= 0 ]
4.43/2.15	
4.43/2.15		start location:	koat_start
4.43/2.15	
4.43/2.15		leaf cost:	0
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	A polynomial rank function with
4.43/2.15	
4.43/2.15		Pol(evaleasy2start) = 2
4.43/2.15	
4.43/2.15		Pol(evaleasy2bb0in) = 2
4.43/2.15	
4.43/2.15		Pol(evaleasy20) = 2
4.43/2.15	
4.43/2.15		Pol(evaleasy21) = 2
4.43/2.15	
4.43/2.15		Pol(evaleasy22) = 2
4.43/2.15	
4.43/2.15		Pol(evaleasy23) = 2
4.43/2.15	
4.43/2.15		Pol(evaleasy24) = 2
4.43/2.15	
4.43/2.15		Pol(evaleasy25) = 2
4.43/2.15	
4.43/2.15		Pol(evaleasy26) = 2
4.43/2.15	
4.43/2.15		Pol(evaleasy2bb1in) = 2
4.43/2.15	
4.43/2.15		Pol(evaleasy2bb2in) = 2
4.43/2.15	
4.43/2.15		Pol(evaleasy2bb3in) = 1
4.43/2.15	
4.43/2.15		Pol(evaleasy2stop) = 0
4.43/2.15	
4.43/2.15		Pol(koat_start) = 2
4.43/2.15	
4.43/2.15	orients all transitions weakly and the transitions
4.43/2.15	
4.43/2.15		evaleasy2bb3in(ar_0, ar_1) -> Com_1(evaleasy2stop(ar_0, ar_1))
4.43/2.15	
4.43/2.15		evaleasy2bb1in(ar_0, ar_1) -> Com_1(evaleasy2bb3in(ar_0, ar_1)) [ 0 >= ar_0 ]
4.43/2.15	
4.43/2.15	strictly and produces the following problem:
4.43/2.15	
4.43/2.15	3:	T:
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy2start(ar_0, ar_1) -> Com_1(evaleasy2bb0in(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy2bb0in(ar_0, ar_1) -> Com_1(evaleasy20(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy20(ar_0, ar_1) -> Com_1(evaleasy21(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy21(ar_0, ar_1) -> Com_1(evaleasy22(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy22(ar_0, ar_1) -> Com_1(evaleasy23(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy23(ar_0, ar_1) -> Com_1(evaleasy24(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy24(ar_0, ar_1) -> Com_1(evaleasy25(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy25(ar_0, ar_1) -> Com_1(evaleasy26(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)    evaleasy26(ar_0, ar_1) -> Com_1(evaleasy2bb1in(ar_1, ar_1))
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy2bb1in(ar_0, ar_1) -> Com_1(evaleasy2bb2in(ar_0, ar_1)) [ ar_0 >= 1 ]
4.43/2.15	
4.43/2.15			(Comp: 2, Cost: 1)    evaleasy2bb1in(ar_0, ar_1) -> Com_1(evaleasy2bb3in(ar_0, ar_1)) [ 0 >= ar_0 ]
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)    evaleasy2bb2in(ar_0, ar_1) -> Com_1(evaleasy2bb1in(ar_0 - 1, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 2, Cost: 1)    evaleasy2bb3in(ar_0, ar_1) -> Com_1(evaleasy2stop(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evaleasy2start(ar_0, ar_1)) [ 0 <= 0 ]
4.43/2.15	
4.43/2.15		start location:	koat_start
4.43/2.15	
4.43/2.15		leaf cost:	0
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	A polynomial rank function with
4.43/2.15	
4.43/2.15		Pol(evaleasy2start) = V_2 + 1
4.43/2.15	
4.43/2.15		Pol(evaleasy2bb0in) = V_2 + 1
4.43/2.15	
4.43/2.15		Pol(evaleasy20) = V_2 + 1
4.43/2.15	
4.43/2.15		Pol(evaleasy21) = V_2 + 1
4.43/2.15	
4.43/2.15		Pol(evaleasy22) = V_2 + 1
4.43/2.15	
4.43/2.15		Pol(evaleasy23) = V_2 + 1
4.43/2.15	
4.43/2.15		Pol(evaleasy24) = V_2 + 1
4.43/2.15	
4.43/2.15		Pol(evaleasy25) = V_2 + 1
4.43/2.15	
4.43/2.15		Pol(evaleasy26) = V_2 + 1
4.43/2.15	
4.43/2.15		Pol(evaleasy2bb1in) = V_1 + 1
4.43/2.15	
4.43/2.15		Pol(evaleasy2bb2in) = V_1
4.43/2.15	
4.43/2.15		Pol(evaleasy2bb3in) = V_1
4.43/2.15	
4.43/2.15		Pol(evaleasy2stop) = V_1
4.43/2.15	
4.43/2.15		Pol(koat_start) = V_2 + 1
4.43/2.15	
4.43/2.15	orients all transitions weakly and the transition
4.43/2.15	
4.43/2.15		evaleasy2bb1in(ar_0, ar_1) -> Com_1(evaleasy2bb2in(ar_0, ar_1)) [ ar_0 >= 1 ]
4.43/2.15	
4.43/2.15	strictly and produces the following problem:
4.43/2.15	
4.43/2.15	4:	T:
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy2start(ar_0, ar_1) -> Com_1(evaleasy2bb0in(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy2bb0in(ar_0, ar_1) -> Com_1(evaleasy20(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy20(ar_0, ar_1) -> Com_1(evaleasy21(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy21(ar_0, ar_1) -> Com_1(evaleasy22(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy22(ar_0, ar_1) -> Com_1(evaleasy23(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy23(ar_0, ar_1) -> Com_1(evaleasy24(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy24(ar_0, ar_1) -> Com_1(evaleasy25(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy25(ar_0, ar_1) -> Com_1(evaleasy26(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy26(ar_0, ar_1) -> Com_1(evaleasy2bb1in(ar_1, ar_1))
4.43/2.15	
4.43/2.15			(Comp: ar_1 + 1, Cost: 1)    evaleasy2bb1in(ar_0, ar_1) -> Com_1(evaleasy2bb2in(ar_0, ar_1)) [ ar_0 >= 1 ]
4.43/2.15	
4.43/2.15			(Comp: 2, Cost: 1)           evaleasy2bb1in(ar_0, ar_1) -> Com_1(evaleasy2bb3in(ar_0, ar_1)) [ 0 >= ar_0 ]
4.43/2.15	
4.43/2.15			(Comp: ?, Cost: 1)           evaleasy2bb2in(ar_0, ar_1) -> Com_1(evaleasy2bb1in(ar_0 - 1, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 2, Cost: 1)           evaleasy2bb3in(ar_0, ar_1) -> Com_1(evaleasy2stop(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1) -> Com_1(evaleasy2start(ar_0, ar_1)) [ 0 <= 0 ]
4.43/2.15	
4.43/2.15		start location:	koat_start
4.43/2.15	
4.43/2.15		leaf cost:	0
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	Repeatedly propagating knowledge in problem 4 produces the following problem:
4.43/2.15	
4.43/2.15	5:	T:
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy2start(ar_0, ar_1) -> Com_1(evaleasy2bb0in(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy2bb0in(ar_0, ar_1) -> Com_1(evaleasy20(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy20(ar_0, ar_1) -> Com_1(evaleasy21(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy21(ar_0, ar_1) -> Com_1(evaleasy22(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy22(ar_0, ar_1) -> Com_1(evaleasy23(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy23(ar_0, ar_1) -> Com_1(evaleasy24(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy24(ar_0, ar_1) -> Com_1(evaleasy25(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy25(ar_0, ar_1) -> Com_1(evaleasy26(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 1)           evaleasy26(ar_0, ar_1) -> Com_1(evaleasy2bb1in(ar_1, ar_1))
4.43/2.15	
4.43/2.15			(Comp: ar_1 + 1, Cost: 1)    evaleasy2bb1in(ar_0, ar_1) -> Com_1(evaleasy2bb2in(ar_0, ar_1)) [ ar_0 >= 1 ]
4.43/2.15	
4.43/2.15			(Comp: 2, Cost: 1)           evaleasy2bb1in(ar_0, ar_1) -> Com_1(evaleasy2bb3in(ar_0, ar_1)) [ 0 >= ar_0 ]
4.43/2.15	
4.43/2.15			(Comp: ar_1 + 1, Cost: 1)    evaleasy2bb2in(ar_0, ar_1) -> Com_1(evaleasy2bb1in(ar_0 - 1, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 2, Cost: 1)           evaleasy2bb3in(ar_0, ar_1) -> Com_1(evaleasy2stop(ar_0, ar_1))
4.43/2.15	
4.43/2.15			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1) -> Com_1(evaleasy2start(ar_0, ar_1)) [ 0 <= 0 ]
4.43/2.15	
4.43/2.15		start location:	koat_start
4.43/2.15	
4.43/2.15		leaf cost:	0
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	Complexity upper bound 2*ar_1 + 15
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	Time: 0.064 sec (SMT: 0.056 sec)
4.43/2.15	
4.43/2.15	
4.43/2.15	----------------------------------------
4.43/2.15	
4.43/2.15	(2)
4.43/2.15	BOUNDS(1, n^1)
4.43/2.15	
4.43/2.15	----------------------------------------
4.43/2.15	
4.43/2.15	(3) Loat Proof (FINISHED)
4.43/2.15	
4.43/2.15	
4.43/2.15	### Pre-processing the ITS problem ###
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	Initial linear ITS problem
4.43/2.15	
4.43/2.15	   Start location: evaleasy2start
4.43/2.15	
4.43/2.15	      0: evaleasy2start -> evaleasy2bb0in : [], cost: 1
4.43/2.15	
4.43/2.15	      1: evaleasy2bb0in -> evaleasy20 : [], cost: 1
4.43/2.15	
4.43/2.15	      2: evaleasy20 -> evaleasy21 : [], cost: 1
4.43/2.15	
4.43/2.15	      3: evaleasy21 -> evaleasy22 : [], cost: 1
4.43/2.15	
4.43/2.15	      4: evaleasy22 -> evaleasy23 : [], cost: 1
4.43/2.15	
4.43/2.15	      5: evaleasy23 -> evaleasy24 : [], cost: 1
4.43/2.15	
4.43/2.15	      6: evaleasy24 -> evaleasy25 : [], cost: 1
4.43/2.15	
4.43/2.15	      7: evaleasy25 -> evaleasy26 : [], cost: 1
4.43/2.15	
4.43/2.15	      8: evaleasy26 -> evaleasy2bb1in : A'=B, [], cost: 1
4.43/2.15	
4.43/2.15	      9: evaleasy2bb1in -> evaleasy2bb2in : [ A>=1 ], cost: 1
4.43/2.15	
4.43/2.15	     10: evaleasy2bb1in -> evaleasy2bb3in : [ 0>=A ], cost: 1
4.43/2.15	
4.43/2.15	     11: evaleasy2bb2in -> evaleasy2bb1in : A'=-1+A, [], cost: 1
4.43/2.15	
4.43/2.15	     12: evaleasy2bb3in -> evaleasy2stop : [], cost: 1
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	Removed unreachable and leaf rules:
4.43/2.15	
4.43/2.15	   Start location: evaleasy2start
4.43/2.15	
4.43/2.15	      0: evaleasy2start -> evaleasy2bb0in : [], cost: 1
4.43/2.15	
4.43/2.15	      1: evaleasy2bb0in -> evaleasy20 : [], cost: 1
4.43/2.15	
4.43/2.15	      2: evaleasy20 -> evaleasy21 : [], cost: 1
4.43/2.15	
4.43/2.15	      3: evaleasy21 -> evaleasy22 : [], cost: 1
4.43/2.15	
4.43/2.15	      4: evaleasy22 -> evaleasy23 : [], cost: 1
4.43/2.15	
4.43/2.15	      5: evaleasy23 -> evaleasy24 : [], cost: 1
4.43/2.15	
4.43/2.15	      6: evaleasy24 -> evaleasy25 : [], cost: 1
4.43/2.15	
4.43/2.15	      7: evaleasy25 -> evaleasy26 : [], cost: 1
4.43/2.15	
4.43/2.15	      8: evaleasy26 -> evaleasy2bb1in : A'=B, [], cost: 1
4.43/2.15	
4.43/2.15	      9: evaleasy2bb1in -> evaleasy2bb2in : [ A>=1 ], cost: 1
4.43/2.15	
4.43/2.15	     11: evaleasy2bb2in -> evaleasy2bb1in : A'=-1+A, [], cost: 1
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	### Simplification by acceleration and chaining ###
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	Eliminated locations (on linear paths):
4.43/2.15	
4.43/2.15	   Start location: evaleasy2start
4.43/2.15	
4.43/2.15	     20: evaleasy2start -> evaleasy2bb1in : A'=B, [], cost: 9
4.43/2.15	
4.43/2.15	     21: evaleasy2bb1in -> evaleasy2bb1in : A'=-1+A, [ A>=1 ], cost: 2
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	Accelerating simple loops of location 9.
4.43/2.15	
4.43/2.15	   Accelerating the following rules:
4.43/2.15	
4.43/2.15	     21: evaleasy2bb1in -> evaleasy2bb1in : A'=-1+A, [ A>=1 ], cost: 2
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	   Accelerated rule 21 with metering function A, yielding the new rule 22.
4.43/2.15	
4.43/2.15	   Removing the simple loops: 21.
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	Accelerated all simple loops using metering functions (where possible):
4.43/2.15	
4.43/2.15	   Start location: evaleasy2start
4.43/2.15	
4.43/2.15	     20: evaleasy2start -> evaleasy2bb1in : A'=B, [], cost: 9
4.43/2.15	
4.43/2.15	     22: evaleasy2bb1in -> evaleasy2bb1in : A'=0, [ A>=1 ], cost: 2*A
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	Chained accelerated rules (with incoming rules):
4.43/2.15	
4.43/2.15	   Start location: evaleasy2start
4.43/2.15	
4.43/2.15	     20: evaleasy2start -> evaleasy2bb1in : A'=B, [], cost: 9
4.43/2.15	
4.43/2.15	     23: evaleasy2start -> evaleasy2bb1in : A'=0, [ B>=1 ], cost: 9+2*B
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	Removed unreachable locations (and leaf rules with constant cost):
4.43/2.15	
4.43/2.15	   Start location: evaleasy2start
4.43/2.15	
4.43/2.15	     23: evaleasy2start -> evaleasy2bb1in : A'=0, [ B>=1 ], cost: 9+2*B
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	### Computing asymptotic complexity ###
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	Fully simplified ITS problem
4.43/2.15	
4.43/2.15	   Start location: evaleasy2start
4.43/2.15	
4.43/2.15	     23: evaleasy2start -> evaleasy2bb1in : A'=0, [ B>=1 ], cost: 9+2*B
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	Computing asymptotic complexity for rule 23
4.43/2.15	
4.43/2.15	   Solved the limit problem by the following transformations:
4.43/2.15	
4.43/2.15	      Created initial limit problem:
4.43/2.15	
4.43/2.15	      9+2*B (+), B (+/+!) [not solved]
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	      removing all constraints (solved by SMT)
4.43/2.15	
4.43/2.15	      resulting limit problem: [solved]
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	      applying transformation rule (C) using substitution {B==n}
4.43/2.15	
4.43/2.15	      resulting limit problem:
4.43/2.15	
4.43/2.15	      [solved]
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	   Solution:
4.43/2.15	
4.43/2.15	      B / n
4.43/2.15	
4.43/2.15	   Resulting cost 9+2*n has complexity: Poly(n^1)
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	Found new complexity Poly(n^1).
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	Obtained the following overall complexity (w.r.t. the length of the input n):
4.43/2.15	
4.43/2.15	   Complexity:  Poly(n^1)
4.43/2.15	
4.43/2.15	   Cpx degree:  1
4.43/2.15	
4.43/2.15	   Solved cost: 9+2*n
4.43/2.15	
4.43/2.15	   Rule cost:   9+2*B
4.43/2.15	
4.43/2.15	   Rule guard:  [ B>=1 ]
4.43/2.15	
4.43/2.15	
4.43/2.15	
4.43/2.15	WORST_CASE(Omega(n^1),?)
4.43/2.15	
4.43/2.15	
4.43/2.15	----------------------------------------
4.43/2.15	
4.43/2.15	(4)
4.43/2.15	BOUNDS(n^1, INF)
4.43/2.17	EOF