3.75/2.17	WORST_CASE(Omega(n^1), O(n^1))
4.64/2.18	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.64/2.18	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.64/2.18	
4.64/2.18	
4.64/2.18	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
4.64/2.18	
4.64/2.18	(0) CpxIntTrs
4.64/2.18	(1) Koat Proof [FINISHED, 10 ms]
4.64/2.18	(2) BOUNDS(1, n^1)
4.64/2.18	(3) Loat Proof [FINISHED, 409 ms]
4.64/2.18	(4) BOUNDS(n^1, INF)
4.64/2.18	
4.64/2.18	
4.64/2.18	----------------------------------------
4.64/2.18	
4.64/2.18	(0)
4.64/2.18	Obligation:
4.64/2.18	Complexity Int TRS consisting of the following rules:
4.64/2.18	eval_abc_start(v_a, v_b, v_i_0) -> Com_1(eval_abc_bb0_in(v_a, v_b, v_i_0)) :|: TRUE
4.64/2.18	eval_abc_bb0_in(v_a, v_b, v_i_0) -> Com_1(eval_abc_0(v_a, v_b, v_i_0)) :|: TRUE
4.64/2.18	eval_abc_0(v_a, v_b, v_i_0) -> Com_1(eval_abc_1(v_a, v_b, v_i_0)) :|: TRUE
4.64/2.18	eval_abc_1(v_a, v_b, v_i_0) -> Com_1(eval_abc_2(v_a, v_b, v_i_0)) :|: TRUE
4.64/2.18	eval_abc_2(v_a, v_b, v_i_0) -> Com_1(eval_abc_3(v_a, v_b, v_i_0)) :|: TRUE
4.64/2.18	eval_abc_3(v_a, v_b, v_i_0) -> Com_1(eval_abc_4(v_a, v_b, v_i_0)) :|: TRUE
4.64/2.18	eval_abc_4(v_a, v_b, v_i_0) -> Com_1(eval_abc_bb1_in(v_a, v_b, v_a)) :|: TRUE
4.64/2.18	eval_abc_bb1_in(v_a, v_b, v_i_0) -> Com_1(eval_abc_bb2_in(v_a, v_b, v_i_0)) :|: v_i_0 <= v_b
4.64/2.18	eval_abc_bb1_in(v_a, v_b, v_i_0) -> Com_1(eval_abc_bb3_in(v_a, v_b, v_i_0)) :|: v_i_0 > v_b
4.64/2.18	eval_abc_bb2_in(v_a, v_b, v_i_0) -> Com_1(eval_abc_bb1_in(v_a, v_b, v_i_0 + 1)) :|: TRUE
4.64/2.18	eval_abc_bb3_in(v_a, v_b, v_i_0) -> Com_1(eval_abc_stop(v_a, v_b, v_i_0)) :|: TRUE
4.64/2.18	
4.64/2.18	The start-symbols are:[eval_abc_start_3]
4.64/2.18	
4.64/2.18	
4.64/2.18	----------------------------------------
4.64/2.18	
4.64/2.18	(1) Koat Proof (FINISHED)
4.64/2.18	YES(?, 2*ar_1 + 2*ar_2 + 13)
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	Initial complexity problem:
4.64/2.18	
4.64/2.18	1:	T:
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)    evalabcstart(ar_0, ar_1, ar_2) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)    evalabcbb0in(ar_0, ar_1, ar_2) -> Com_1(evalabc0(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)    evalabc0(ar_0, ar_1, ar_2) -> Com_1(evalabc1(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)    evalabc1(ar_0, ar_1, ar_2) -> Com_1(evalabc2(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)    evalabc2(ar_0, ar_1, ar_2) -> Com_1(evalabc3(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)    evalabc3(ar_0, ar_1, ar_2) -> Com_1(evalabc4(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)    evalabc4(ar_0, ar_1, ar_2) -> Com_1(evalabcbb1in(ar_1, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)    evalabcbb1in(ar_0, ar_1, ar_2) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)    evalabcbb1in(ar_0, ar_1, ar_2) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)    evalabcbb2in(ar_0, ar_1, ar_2) -> Com_1(evalabcbb1in(ar_0 + 1, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)    evalabcbb3in(ar_0, ar_1, ar_2) -> Com_1(evalabcstop(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalabcstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.64/2.18	
4.64/2.18		start location:	koat_start
4.64/2.18	
4.64/2.18		leaf cost:	0
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	Repeatedly propagating knowledge in problem 1 produces the following problem:
4.64/2.18	
4.64/2.18	2:	T:
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)    evalabcstart(ar_0, ar_1, ar_2) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)    evalabcbb0in(ar_0, ar_1, ar_2) -> Com_1(evalabc0(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)    evalabc0(ar_0, ar_1, ar_2) -> Com_1(evalabc1(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)    evalabc1(ar_0, ar_1, ar_2) -> Com_1(evalabc2(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)    evalabc2(ar_0, ar_1, ar_2) -> Com_1(evalabc3(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)    evalabc3(ar_0, ar_1, ar_2) -> Com_1(evalabc4(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)    evalabc4(ar_0, ar_1, ar_2) -> Com_1(evalabcbb1in(ar_1, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)    evalabcbb1in(ar_0, ar_1, ar_2) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)    evalabcbb1in(ar_0, ar_1, ar_2) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)    evalabcbb2in(ar_0, ar_1, ar_2) -> Com_1(evalabcbb1in(ar_0 + 1, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)    evalabcbb3in(ar_0, ar_1, ar_2) -> Com_1(evalabcstop(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalabcstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.64/2.18	
4.64/2.18		start location:	koat_start
4.64/2.18	
4.64/2.18		leaf cost:	0
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	A polynomial rank function with
4.64/2.18	
4.64/2.18		Pol(evalabcstart) = 2
4.64/2.18	
4.64/2.18		Pol(evalabcbb0in) = 2
4.64/2.18	
4.64/2.18		Pol(evalabc0) = 2
4.64/2.18	
4.64/2.18		Pol(evalabc1) = 2
4.64/2.18	
4.64/2.18		Pol(evalabc2) = 2
4.64/2.18	
4.64/2.18		Pol(evalabc3) = 2
4.64/2.18	
4.64/2.18		Pol(evalabc4) = 2
4.64/2.18	
4.64/2.18		Pol(evalabcbb1in) = 2
4.64/2.18	
4.64/2.18		Pol(evalabcbb2in) = 2
4.64/2.18	
4.64/2.18		Pol(evalabcbb3in) = 1
4.64/2.18	
4.64/2.18		Pol(evalabcstop) = 0
4.64/2.18	
4.64/2.18		Pol(koat_start) = 2
4.64/2.18	
4.64/2.18	orients all transitions weakly and the transitions
4.64/2.18	
4.64/2.18		evalabcbb3in(ar_0, ar_1, ar_2) -> Com_1(evalabcstop(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18		evalabcbb1in(ar_0, ar_1, ar_2) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
4.64/2.18	
4.64/2.18	strictly and produces the following problem:
4.64/2.18	
4.64/2.18	3:	T:
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)    evalabcstart(ar_0, ar_1, ar_2) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)    evalabcbb0in(ar_0, ar_1, ar_2) -> Com_1(evalabc0(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)    evalabc0(ar_0, ar_1, ar_2) -> Com_1(evalabc1(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)    evalabc1(ar_0, ar_1, ar_2) -> Com_1(evalabc2(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)    evalabc2(ar_0, ar_1, ar_2) -> Com_1(evalabc3(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)    evalabc3(ar_0, ar_1, ar_2) -> Com_1(evalabc4(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)    evalabc4(ar_0, ar_1, ar_2) -> Com_1(evalabcbb1in(ar_1, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)    evalabcbb1in(ar_0, ar_1, ar_2) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]
4.64/2.18	
4.64/2.18			(Comp: 2, Cost: 1)    evalabcbb1in(ar_0, ar_1, ar_2) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)    evalabcbb2in(ar_0, ar_1, ar_2) -> Com_1(evalabcbb1in(ar_0 + 1, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 2, Cost: 1)    evalabcbb3in(ar_0, ar_1, ar_2) -> Com_1(evalabcstop(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalabcstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.64/2.18	
4.64/2.18		start location:	koat_start
4.64/2.18	
4.64/2.18		leaf cost:	0
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	A polynomial rank function with
4.64/2.18	
4.64/2.18		Pol(evalabcstart) = -V_2 + V_3 + 1
4.64/2.18	
4.64/2.18		Pol(evalabcbb0in) = -V_2 + V_3 + 1
4.64/2.18	
4.64/2.18		Pol(evalabc0) = -V_2 + V_3 + 1
4.64/2.18	
4.64/2.18		Pol(evalabc1) = -V_2 + V_3 + 1
4.64/2.18	
4.64/2.18		Pol(evalabc2) = -V_2 + V_3 + 1
4.64/2.18	
4.64/2.18		Pol(evalabc3) = -V_2 + V_3 + 1
4.64/2.18	
4.64/2.18		Pol(evalabc4) = -V_2 + V_3 + 1
4.64/2.18	
4.64/2.18		Pol(evalabcbb1in) = -V_1 + V_3 + 1
4.64/2.18	
4.64/2.18		Pol(evalabcbb2in) = -V_1 + V_3
4.64/2.18	
4.64/2.18		Pol(evalabcbb3in) = -V_1 + V_3
4.64/2.18	
4.64/2.18		Pol(evalabcstop) = -V_1 + V_3
4.64/2.18	
4.64/2.18		Pol(koat_start) = -V_2 + V_3 + 1
4.64/2.18	
4.64/2.18	orients all transitions weakly and the transition
4.64/2.18	
4.64/2.18		evalabcbb1in(ar_0, ar_1, ar_2) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]
4.64/2.18	
4.64/2.18	strictly and produces the following problem:
4.64/2.18	
4.64/2.18	4:	T:
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)                  evalabcstart(ar_0, ar_1, ar_2) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)                  evalabcbb0in(ar_0, ar_1, ar_2) -> Com_1(evalabc0(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)                  evalabc0(ar_0, ar_1, ar_2) -> Com_1(evalabc1(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)                  evalabc1(ar_0, ar_1, ar_2) -> Com_1(evalabc2(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)                  evalabc2(ar_0, ar_1, ar_2) -> Com_1(evalabc3(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)                  evalabc3(ar_0, ar_1, ar_2) -> Com_1(evalabc4(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)                  evalabc4(ar_0, ar_1, ar_2) -> Com_1(evalabcbb1in(ar_1, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: ar_1 + ar_2 + 1, Cost: 1)    evalabcbb1in(ar_0, ar_1, ar_2) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]
4.64/2.18	
4.64/2.18			(Comp: 2, Cost: 1)                  evalabcbb1in(ar_0, ar_1, ar_2) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
4.64/2.18	
4.64/2.18			(Comp: ?, Cost: 1)                  evalabcbb2in(ar_0, ar_1, ar_2) -> Com_1(evalabcbb1in(ar_0 + 1, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 2, Cost: 1)                  evalabcbb3in(ar_0, ar_1, ar_2) -> Com_1(evalabcstop(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 0)                  koat_start(ar_0, ar_1, ar_2) -> Com_1(evalabcstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.64/2.18	
4.64/2.18		start location:	koat_start
4.64/2.18	
4.64/2.18		leaf cost:	0
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	Repeatedly propagating knowledge in problem 4 produces the following problem:
4.64/2.18	
4.64/2.18	5:	T:
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)                  evalabcstart(ar_0, ar_1, ar_2) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)                  evalabcbb0in(ar_0, ar_1, ar_2) -> Com_1(evalabc0(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)                  evalabc0(ar_0, ar_1, ar_2) -> Com_1(evalabc1(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)                  evalabc1(ar_0, ar_1, ar_2) -> Com_1(evalabc2(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)                  evalabc2(ar_0, ar_1, ar_2) -> Com_1(evalabc3(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)                  evalabc3(ar_0, ar_1, ar_2) -> Com_1(evalabc4(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 1)                  evalabc4(ar_0, ar_1, ar_2) -> Com_1(evalabcbb1in(ar_1, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: ar_1 + ar_2 + 1, Cost: 1)    evalabcbb1in(ar_0, ar_1, ar_2) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]
4.64/2.18	
4.64/2.18			(Comp: 2, Cost: 1)                  evalabcbb1in(ar_0, ar_1, ar_2) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
4.64/2.18	
4.64/2.18			(Comp: ar_1 + ar_2 + 1, Cost: 1)    evalabcbb2in(ar_0, ar_1, ar_2) -> Com_1(evalabcbb1in(ar_0 + 1, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 2, Cost: 1)                  evalabcbb3in(ar_0, ar_1, ar_2) -> Com_1(evalabcstop(ar_0, ar_1, ar_2))
4.64/2.18	
4.64/2.18			(Comp: 1, Cost: 0)                  koat_start(ar_0, ar_1, ar_2) -> Com_1(evalabcstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.64/2.18	
4.64/2.18		start location:	koat_start
4.64/2.18	
4.64/2.18		leaf cost:	0
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	Complexity upper bound 2*ar_1 + 2*ar_2 + 13
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	Time: 0.078 sec (SMT: 0.067 sec)
4.64/2.18	
4.64/2.18	
4.64/2.18	----------------------------------------
4.64/2.18	
4.64/2.18	(2)
4.64/2.18	BOUNDS(1, n^1)
4.64/2.18	
4.64/2.18	----------------------------------------
4.64/2.18	
4.64/2.18	(3) Loat Proof (FINISHED)
4.64/2.18	
4.64/2.18	
4.64/2.18	### Pre-processing the ITS problem ###
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	Initial linear ITS problem
4.64/2.18	
4.64/2.18	   Start location: evalabcstart
4.64/2.18	
4.64/2.18	      0: evalabcstart -> evalabcbb0in : [], cost: 1
4.64/2.18	
4.64/2.18	      1: evalabcbb0in -> evalabc0 : [], cost: 1
4.64/2.18	
4.64/2.18	      2: evalabc0 -> evalabc1 : [], cost: 1
4.64/2.18	
4.64/2.18	      3: evalabc1 -> evalabc2 : [], cost: 1
4.64/2.18	
4.64/2.18	      4: evalabc2 -> evalabc3 : [], cost: 1
4.64/2.18	
4.64/2.18	      5: evalabc3 -> evalabc4 : [], cost: 1
4.64/2.18	
4.64/2.18	      6: evalabc4 -> evalabcbb1in : A'=B, [], cost: 1
4.64/2.18	
4.64/2.18	      7: evalabcbb1in -> evalabcbb2in : [ C>=A ], cost: 1
4.64/2.18	
4.64/2.18	      8: evalabcbb1in -> evalabcbb3in : [ A>=1+C ], cost: 1
4.64/2.18	
4.64/2.18	      9: evalabcbb2in -> evalabcbb1in : A'=1+A, [], cost: 1
4.64/2.18	
4.64/2.18	     10: evalabcbb3in -> evalabcstop : [], cost: 1
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	Removed unreachable and leaf rules:
4.64/2.18	
4.64/2.18	   Start location: evalabcstart
4.64/2.18	
4.64/2.18	      0: evalabcstart -> evalabcbb0in : [], cost: 1
4.64/2.18	
4.64/2.18	      1: evalabcbb0in -> evalabc0 : [], cost: 1
4.64/2.18	
4.64/2.18	      2: evalabc0 -> evalabc1 : [], cost: 1
4.64/2.18	
4.64/2.18	      3: evalabc1 -> evalabc2 : [], cost: 1
4.64/2.18	
4.64/2.18	      4: evalabc2 -> evalabc3 : [], cost: 1
4.64/2.18	
4.64/2.18	      5: evalabc3 -> evalabc4 : [], cost: 1
4.64/2.18	
4.64/2.18	      6: evalabc4 -> evalabcbb1in : A'=B, [], cost: 1
4.64/2.18	
4.64/2.18	      7: evalabcbb1in -> evalabcbb2in : [ C>=A ], cost: 1
4.64/2.18	
4.64/2.18	      9: evalabcbb2in -> evalabcbb1in : A'=1+A, [], cost: 1
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	### Simplification by acceleration and chaining ###
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	Eliminated locations (on linear paths):
4.64/2.18	
4.64/2.18	   Start location: evalabcstart
4.64/2.18	
4.64/2.18	     16: evalabcstart -> evalabcbb1in : A'=B, [], cost: 7
4.64/2.18	
4.64/2.18	     17: evalabcbb1in -> evalabcbb1in : A'=1+A, [ C>=A ], cost: 2
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	Accelerating simple loops of location 7.
4.64/2.18	
4.64/2.18	   Accelerating the following rules:
4.64/2.18	
4.64/2.18	     17: evalabcbb1in -> evalabcbb1in : A'=1+A, [ C>=A ], cost: 2
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	   Accelerated rule 17 with metering function 1+C-A, yielding the new rule 18.
4.64/2.18	
4.64/2.18	   Removing the simple loops: 17.
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	Accelerated all simple loops using metering functions (where possible):
4.64/2.18	
4.64/2.18	   Start location: evalabcstart
4.64/2.18	
4.64/2.18	     16: evalabcstart -> evalabcbb1in : A'=B, [], cost: 7
4.64/2.18	
4.64/2.18	     18: evalabcbb1in -> evalabcbb1in : A'=1+C, [ C>=A ], cost: 2+2*C-2*A
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	Chained accelerated rules (with incoming rules):
4.64/2.18	
4.64/2.18	   Start location: evalabcstart
4.64/2.18	
4.64/2.18	     16: evalabcstart -> evalabcbb1in : A'=B, [], cost: 7
4.64/2.18	
4.64/2.18	     19: evalabcstart -> evalabcbb1in : A'=1+C, [ C>=B ], cost: 9+2*C-2*B
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	Removed unreachable locations (and leaf rules with constant cost):
4.64/2.18	
4.64/2.18	   Start location: evalabcstart
4.64/2.18	
4.64/2.18	     19: evalabcstart -> evalabcbb1in : A'=1+C, [ C>=B ], cost: 9+2*C-2*B
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	### Computing asymptotic complexity ###
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	Fully simplified ITS problem
4.64/2.18	
4.64/2.18	   Start location: evalabcstart
4.64/2.18	
4.64/2.18	     19: evalabcstart -> evalabcbb1in : A'=1+C, [ C>=B ], cost: 9+2*C-2*B
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	Computing asymptotic complexity for rule 19
4.64/2.18	
4.64/2.18	   Solved the limit problem by the following transformations:
4.64/2.18	
4.64/2.18	      Created initial limit problem:
4.64/2.18	
4.64/2.18	      9+2*C-2*B (+), 1+C-B (+/+!) [not solved]
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	      removing all constraints (solved by SMT)
4.64/2.18	
4.64/2.18	      resulting limit problem: [solved]
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	      applying transformation rule (C) using substitution {C==0,B==-n}
4.64/2.18	
4.64/2.18	      resulting limit problem:
4.64/2.18	
4.64/2.18	      [solved]
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	   Solution:
4.64/2.18	
4.64/2.18	      C / 0
4.64/2.18	
4.64/2.18	      B / -n
4.64/2.18	
4.64/2.18	   Resulting cost 9+2*n has complexity: Poly(n^1)
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	Found new complexity Poly(n^1).
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	Obtained the following overall complexity (w.r.t. the length of the input n):
4.64/2.18	
4.64/2.18	   Complexity:  Poly(n^1)
4.64/2.18	
4.64/2.18	   Cpx degree:  1
4.64/2.18	
4.64/2.18	   Solved cost: 9+2*n
4.64/2.18	
4.64/2.18	   Rule cost:   9+2*C-2*B
4.64/2.18	
4.64/2.18	   Rule guard:  [ C>=B ]
4.64/2.18	
4.64/2.18	
4.64/2.18	
4.64/2.18	WORST_CASE(Omega(n^1),?)
4.64/2.18	
4.64/2.18	
4.64/2.18	----------------------------------------
4.64/2.18	
4.64/2.18	(4)
4.64/2.18	BOUNDS(n^1, INF)
4.64/2.21	EOF