5.24/2.41	WORST_CASE(Omega(n^2), O(n^2))
5.28/2.42	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.28/2.42	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.28/2.42	
5.28/2.42	
5.28/2.42	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).
5.28/2.42	
5.28/2.42	(0) CpxIntTrs
5.28/2.42	(1) Koat Proof [FINISHED, 214 ms]
5.28/2.42	(2) BOUNDS(1, n^2)
5.28/2.42	(3) Loat Proof [FINISHED, 834 ms]
5.28/2.42	(4) BOUNDS(n^2, INF)
5.28/2.42	
5.28/2.42	
5.28/2.42	----------------------------------------
5.28/2.42	
5.28/2.42	(0)
5.28/2.42	Obligation:
5.28/2.42	Complexity Int TRS consisting of the following rules:
5.28/2.42	eval_abc_start(v_3, v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_abc_bb0_in(v_3, v_i_0, v_j_0, v_m, v_n)) :|: TRUE
5.28/2.42	eval_abc_bb0_in(v_3, v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_abc_0(v_3, v_i_0, v_j_0, v_m, v_n)) :|: TRUE
5.28/2.42	eval_abc_0(v_3, v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_abc_1(v_3, v_i_0, v_j_0, v_m, v_n)) :|: TRUE
5.28/2.42	eval_abc_1(v_3, v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_abc_2(v_3, v_i_0, v_j_0, v_m, v_n)) :|: TRUE
5.28/2.42	eval_abc_2(v_3, v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_abc_3(v_3, v_i_0, v_j_0, v_m, v_n)) :|: TRUE
5.28/2.42	eval_abc_3(v_3, v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_abc_4(v_3, v_i_0, v_j_0, v_m, v_n)) :|: TRUE
5.28/2.42	eval_abc_4(v_3, v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_abc_5(v_3, v_i_0, v_j_0, v_m, v_n)) :|: TRUE
5.28/2.42	eval_abc_5(v_3, v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_abc_bb1_in(v_3, v_i_0, 1, v_m, v_n)) :|: TRUE
5.28/2.42	eval_abc_bb1_in(v_3, v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_abc_bb2_in(v_3, 1, v_j_0, v_m, v_n)) :|: v_j_0 <= v_n
5.28/2.42	eval_abc_bb1_in(v_3, v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_abc_bb5_in(v_3, v_i_0, v_j_0, v_m, v_n)) :|: v_j_0 > v_n
5.28/2.42	eval_abc_bb2_in(v_3, v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_abc_bb3_in(v_3, v_i_0, v_j_0, v_m, v_n)) :|: v_i_0 <= v_m
5.28/2.42	eval_abc_bb2_in(v_3, v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_abc_bb4_in(v_3, v_i_0, v_j_0, v_m, v_n)) :|: v_i_0 > v_m
5.28/2.42	eval_abc_bb3_in(v_3, v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_abc_bb2_in(v_3, v_i_0 + 1, v_j_0, v_m, v_n)) :|: TRUE
5.28/2.42	eval_abc_bb4_in(v_3, v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_abc_9(v_j_0 + 1, v_i_0, v_j_0, v_m, v_n)) :|: TRUE
5.28/2.42	eval_abc_9(v_3, v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_abc_10(v_3, v_i_0, v_j_0, v_m, v_n)) :|: TRUE
5.28/2.42	eval_abc_10(v_3, v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_abc_bb1_in(v_3, v_i_0, v_3, v_m, v_n)) :|: TRUE
5.28/2.42	eval_abc_bb5_in(v_3, v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_abc_stop(v_3, v_i_0, v_j_0, v_m, v_n)) :|: TRUE
5.28/2.42	
5.28/2.42	The start-symbols are:[eval_abc_start_5]
5.28/2.42	
5.28/2.42	
5.28/2.42	----------------------------------------
5.28/2.42	
5.28/2.42	(1) Koat Proof (FINISHED)
5.28/2.42	YES(?, 21*ar_1 + 2*ar_1*ar_3 + 12)
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Initial complexity problem:
5.28/2.42	
5.28/2.42	1:	T:
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.28/2.42	
5.28/2.42		start location:	koat_start
5.28/2.42	
5.28/2.42		leaf cost:	0
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Repeatedly propagating knowledge in problem 1 produces the following problem:
5.28/2.42	
5.28/2.42	2:	T:
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)    evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)    evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)    evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)    evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)    evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)    evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)    evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)    evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.28/2.42	
5.28/2.42		start location:	koat_start
5.28/2.42	
5.28/2.42		leaf cost:	0
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	A polynomial rank function with
5.28/2.42	
5.28/2.42		Pol(evalabcstart) = 2
5.28/2.42	
5.28/2.42		Pol(evalabcbb0in) = 2
5.28/2.42	
5.28/2.42		Pol(evalabc0) = 2
5.28/2.42	
5.28/2.42		Pol(evalabc1) = 2
5.28/2.42	
5.28/2.42		Pol(evalabc2) = 2
5.28/2.42	
5.28/2.42		Pol(evalabc3) = 2
5.28/2.42	
5.28/2.42		Pol(evalabc4) = 2
5.28/2.42	
5.28/2.42		Pol(evalabc5) = 2
5.28/2.42	
5.28/2.42		Pol(evalabcbb1in) = 2
5.28/2.42	
5.28/2.42		Pol(evalabcbb2in) = 2
5.28/2.42	
5.28/2.42		Pol(evalabcbb5in) = 1
5.28/2.42	
5.28/2.42		Pol(evalabcbb3in) = 2
5.28/2.42	
5.28/2.42		Pol(evalabcbb4in) = 2
5.28/2.42	
5.28/2.42		Pol(evalabc9) = 2
5.28/2.42	
5.28/2.42		Pol(evalabc10) = 2
5.28/2.42	
5.28/2.42		Pol(evalabcstop) = 0
5.28/2.42	
5.28/2.42		Pol(koat_start) = 2
5.28/2.42	
5.28/2.42	orients all transitions weakly and the transitions
5.28/2.42	
5.28/2.42		evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42		evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]
5.28/2.42	
5.28/2.42	strictly and produces the following problem:
5.28/2.42	
5.28/2.42	3:	T:
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)    evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)    evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)    evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)    evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)    evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)    evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)    evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)    evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]
5.28/2.42	
5.28/2.42			(Comp: 2, Cost: 1)    evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)    evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 2, Cost: 1)    evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.28/2.42	
5.28/2.42		start location:	koat_start
5.28/2.42	
5.28/2.42		leaf cost:	0
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	A polynomial rank function with
5.28/2.42	
5.28/2.42		Pol(evalabcstart) = V_2
5.28/2.42	
5.28/2.42		Pol(evalabcbb0in) = V_2
5.28/2.42	
5.28/2.42		Pol(evalabc0) = V_2
5.28/2.42	
5.28/2.42		Pol(evalabc1) = V_2
5.28/2.42	
5.28/2.42		Pol(evalabc2) = V_2
5.28/2.42	
5.28/2.42		Pol(evalabc3) = V_2
5.28/2.42	
5.28/2.42		Pol(evalabc4) = V_2
5.28/2.42	
5.28/2.42		Pol(evalabc5) = V_2
5.28/2.42	
5.28/2.42		Pol(evalabcbb1in) = -V_1 + V_2 + 1
5.28/2.42	
5.28/2.42		Pol(evalabcbb2in) = -V_1 + V_2
5.28/2.42	
5.28/2.42		Pol(evalabcbb5in) = -V_1 + V_2
5.28/2.42	
5.28/2.42		Pol(evalabcbb3in) = -V_1 + V_2
5.28/2.42	
5.28/2.42		Pol(evalabcbb4in) = -V_1 + V_2
5.28/2.42	
5.28/2.42		Pol(evalabc9) = V_2 - V_5 + 1
5.28/2.42	
5.28/2.42		Pol(evalabc10) = V_2 - V_5 + 1
5.28/2.42	
5.28/2.42		Pol(evalabcstop) = -V_1 + V_2
5.28/2.42	
5.28/2.42		Pol(koat_start) = V_2
5.28/2.42	
5.28/2.42	orients all transitions weakly and the transition
5.28/2.42	
5.28/2.42		evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]
5.28/2.42	
5.28/2.42	strictly and produces the following problem:
5.28/2.42	
5.28/2.42	4:	T:
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)       evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)       evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)       evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)       evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)       evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)       evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)       evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)       evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ar_1, Cost: 1)    evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]
5.28/2.42	
5.28/2.42			(Comp: 2, Cost: 1)       evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)       evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)       evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)       evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)       evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)       evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)       evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 2, Cost: 1)       evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.28/2.42	
5.28/2.42		start location:	koat_start
5.28/2.42	
5.28/2.42		leaf cost:	0
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	A polynomial rank function with
5.28/2.42	
5.28/2.42		Pol(evalabcbb4in) = 3
5.28/2.42	
5.28/2.42		Pol(evalabc9) = 2
5.28/2.42	
5.28/2.42		Pol(evalabcbb3in) = 4
5.28/2.42	
5.28/2.42		Pol(evalabcbb2in) = 4
5.28/2.42	
5.28/2.42		Pol(evalabc10) = 1
5.28/2.42	
5.28/2.42		Pol(evalabcbb1in) = 0
5.28/2.42	
5.28/2.42	and size complexities
5.28/2.42	
5.28/2.42		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0
5.28/2.42	
5.28/2.42		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4
5.28/2.42	
5.28/2.42		S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ?
5.28/2.42	
5.28/2.42		S("evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-0) = ?
5.28/2.42	
5.28/2.42		S("evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-2) = ?
5.28/2.42	
5.28/2.42		S("evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-4) = ?
5.28/2.42	
5.28/2.42		S("evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ?
5.28/2.42	
5.28/2.42		S("evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ?
5.28/2.42	
5.28/2.42		S("evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-0) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-2) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-4) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-0) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-2) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-4) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]", 0-0) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]", 0-2) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]", 0-4) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]", 0-0) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]", 0-2) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]", 0-4) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-4) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-0) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-2) = 1
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-4) = ?
5.28/2.42	
5.28/2.42		S("evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-0) = 1
5.28/2.42	
5.28/2.42		S("evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.28/2.42	
5.28/2.42		S("evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.28/2.42	
5.28/2.42		S("evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.28/2.42	
5.28/2.42		S("evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.28/2.42	
5.28/2.42		S("evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.28/2.42	
5.28/2.42		S("evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.28/2.42	
5.28/2.42		S("evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.28/2.42	
5.28/2.42		S("evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.28/2.42	
5.28/2.42		S("evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.28/2.42	
5.28/2.42		S("evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.28/2.42	
5.28/2.42		S("evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.28/2.42	
5.28/2.42		S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.28/2.42	
5.28/2.42		S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.28/2.42	
5.28/2.42		S("evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.28/2.42	
5.28/2.42		S("evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.28/2.42	
5.28/2.42	orients the transitions
5.28/2.42	
5.28/2.42		evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))
5.28/2.42	
5.28/2.42		evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))
5.28/2.42	
5.28/2.42		evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]
5.28/2.42	
5.28/2.42		evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]
5.28/2.42	
5.28/2.42		evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42		evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42	weakly and the transitions
5.28/2.42	
5.28/2.42		evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))
5.28/2.42	
5.28/2.42		evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]
5.28/2.42	
5.28/2.42		evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42		evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42	strictly and produces the following problem:
5.28/2.42	
5.28/2.42	5:	T:
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)         evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)         evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)         evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)         evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)         evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)         evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)         evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)         evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ar_1, Cost: 1)      evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]
5.28/2.42	
5.28/2.42			(Comp: 2, Cost: 1)         evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)         evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]
5.28/2.42	
5.28/2.42			(Comp: 4*ar_1, Cost: 1)    evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)         evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 4*ar_1, Cost: 1)    evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))
5.28/2.42	
5.28/2.42			(Comp: 4*ar_1, Cost: 1)    evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 4*ar_1, Cost: 1)    evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 2, Cost: 1)         evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 0)         koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.28/2.42	
5.28/2.42		start location:	koat_start
5.28/2.42	
5.28/2.42		leaf cost:	0
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	A polynomial rank function with
5.28/2.42	
5.28/2.42		Pol(evalabcbb3in) = -V_3 + V_4
5.28/2.42	
5.28/2.42		Pol(evalabcbb2in) = -V_3 + V_4 + 1
5.28/2.42	
5.28/2.42	and size complexities
5.28/2.42	
5.28/2.42		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0
5.28/2.42	
5.28/2.42		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4
5.28/2.42	
5.28/2.42		S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = 4*ar_1 + 272
5.28/2.42	
5.28/2.42		S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = 4*ar_1 + 4*ar_4 + 1024
5.28/2.42	
5.28/2.42		S("evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-0) = 4*ar_1 + 16
5.28/2.42	
5.28/2.42		S("evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-2) = ?
5.28/2.42	
5.28/2.42		S("evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-4) = 4*ar_1 + 64
5.28/2.42	
5.28/2.42		S("evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = 4*ar_1 + 256
5.28/2.42	
5.28/2.42		S("evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ?
5.28/2.42	
5.28/2.42		S("evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = 4*ar_1 + 16
5.28/2.42	
5.28/2.42		S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-0) = 4*ar_1 + 64
5.28/2.42	
5.28/2.42		S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-2) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-4) = 4*ar_1 + 16
5.28/2.42	
5.28/2.42		S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-0) = 4*ar_1 + 16
5.28/2.42	
5.28/2.42		S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-2) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-4) = 4*ar_1 + 4*ar_4 + 1024
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]", 0-0) = 4*ar_1 + 16
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]", 0-2) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]", 0-4) = 4*ar_1 + 4*ar_4 + 4096
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]", 0-0) = 4*ar_1 + 16
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]", 0-2) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]", 0-4) = 4*ar_1 + 4*ar_4 + 1024
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-0) = 4*ar_1 + 68
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ?
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-4) = 4*ar_1 + 4*ar_4 + 256
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-0) = 4*ar_1 + 16
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-2) = 1
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-4) = 4*ar_1 + 4*ar_4 + 256
5.28/2.42	
5.28/2.42		S("evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-0) = 1
5.28/2.42	
5.28/2.42		S("evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.28/2.42	
5.28/2.42		S("evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.28/2.42	
5.28/2.42		S("evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.28/2.42	
5.28/2.42		S("evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.28/2.42	
5.28/2.42		S("evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.28/2.42	
5.28/2.42		S("evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.28/2.42	
5.28/2.42		S("evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.28/2.42	
5.28/2.42		S("evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.28/2.42	
5.28/2.42		S("evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.28/2.42	
5.28/2.42		S("evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.28/2.42	
5.28/2.42		S("evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.28/2.42	
5.28/2.42		S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.28/2.42	
5.28/2.42		S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.28/2.42	
5.28/2.42		S("evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.28/2.42	
5.28/2.42		S("evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.28/2.42	
5.28/2.42		S("evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.28/2.42	
5.28/2.42		S("evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.28/2.42	
5.28/2.42		S("evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.28/2.42	
5.28/2.42	orients the transitions
5.28/2.42	
5.28/2.42		evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))
5.28/2.42	
5.28/2.42		evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]
5.28/2.42	
5.28/2.42	weakly and the transition
5.28/2.42	
5.28/2.42		evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]
5.28/2.42	
5.28/2.42	strictly and produces the following problem:
5.28/2.42	
5.28/2.42	6:	T:
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)                     evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)                     evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)                     evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)                     evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)                     evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)                     evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)                     evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)                     evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ar_1, Cost: 1)                  evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]
5.28/2.42	
5.28/2.42			(Comp: 2, Cost: 1)                     evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]
5.28/2.42	
5.28/2.42			(Comp: ar_1*ar_3 + 2*ar_1, Cost: 1)    evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]
5.28/2.42	
5.28/2.42			(Comp: 4*ar_1, Cost: 1)                evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]
5.28/2.42	
5.28/2.42			(Comp: ?, Cost: 1)                     evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 4*ar_1, Cost: 1)                evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))
5.28/2.42	
5.28/2.42			(Comp: 4*ar_1, Cost: 1)                evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 4*ar_1, Cost: 1)                evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 2, Cost: 1)                     evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 0)                     koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.28/2.42	
5.28/2.42		start location:	koat_start
5.28/2.42	
5.28/2.42		leaf cost:	0
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Repeatedly propagating knowledge in problem 6 produces the following problem:
5.28/2.42	
5.28/2.42	7:	T:
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)                     evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)                     evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)                     evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)                     evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)                     evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)                     evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)                     evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 1)                     evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: ar_1, Cost: 1)                  evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ]
5.28/2.42	
5.28/2.42			(Comp: 2, Cost: 1)                     evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]
5.28/2.42	
5.28/2.42			(Comp: ar_1*ar_3 + 2*ar_1, Cost: 1)    evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]
5.28/2.42	
5.28/2.42			(Comp: 4*ar_1, Cost: 1)                evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 + 1 ]
5.28/2.42	
5.28/2.42			(Comp: ar_1*ar_3 + 2*ar_1, Cost: 1)    evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 4*ar_1, Cost: 1)                evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))
5.28/2.42	
5.28/2.42			(Comp: 4*ar_1, Cost: 1)                evalabc9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 4*ar_1, Cost: 1)                evalabc10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 2, Cost: 1)                     evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.28/2.42	
5.28/2.42			(Comp: 1, Cost: 0)                     koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.28/2.42	
5.28/2.42		start location:	koat_start
5.28/2.42	
5.28/2.42		leaf cost:	0
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Complexity upper bound 21*ar_1 + 2*ar_1*ar_3 + 12
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Time: 0.217 sec (SMT: 0.152 sec)
5.28/2.42	
5.28/2.42	
5.28/2.42	----------------------------------------
5.28/2.42	
5.28/2.42	(2)
5.28/2.42	BOUNDS(1, n^2)
5.28/2.42	
5.28/2.42	----------------------------------------
5.28/2.42	
5.28/2.42	(3) Loat Proof (FINISHED)
5.28/2.42	
5.28/2.42	
5.28/2.42	### Pre-processing the ITS problem ###
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Initial linear ITS problem
5.28/2.42	
5.28/2.42	   Start location: evalabcstart
5.28/2.42	
5.28/2.42	      0: evalabcstart -> evalabcbb0in : [], cost: 1
5.28/2.42	
5.28/2.42	      1: evalabcbb0in -> evalabc0 : [], cost: 1
5.28/2.42	
5.28/2.42	      2: evalabc0 -> evalabc1 : [], cost: 1
5.28/2.42	
5.28/2.42	      3: evalabc1 -> evalabc2 : [], cost: 1
5.28/2.42	
5.28/2.42	      4: evalabc2 -> evalabc3 : [], cost: 1
5.28/2.42	
5.28/2.42	      5: evalabc3 -> evalabc4 : [], cost: 1
5.28/2.42	
5.28/2.42	      6: evalabc4 -> evalabc5 : [], cost: 1
5.28/2.42	
5.28/2.42	      7: evalabc5 -> evalabcbb1in : A'=1, [], cost: 1
5.28/2.42	
5.28/2.42	      8: evalabcbb1in -> evalabcbb2in : C'=1, [ B>=A ], cost: 1
5.28/2.42	
5.28/2.42	      9: evalabcbb1in -> evalabcbb5in : [ A>=1+B ], cost: 1
5.28/2.42	
5.28/2.42	     10: evalabcbb2in -> evalabcbb3in : [ D>=C ], cost: 1
5.28/2.42	
5.28/2.42	     11: evalabcbb2in -> evalabcbb4in : [ C>=1+D ], cost: 1
5.28/2.42	
5.28/2.42	     12: evalabcbb3in -> evalabcbb2in : C'=1+C, [], cost: 1
5.28/2.42	
5.28/2.42	     13: evalabcbb4in -> evalabc9 : E'=1+A, [], cost: 1
5.28/2.42	
5.28/2.42	     14: evalabc9 -> evalabc10 : [], cost: 1
5.28/2.42	
5.28/2.42	     15: evalabc10 -> evalabcbb1in : A'=E, [], cost: 1
5.28/2.42	
5.28/2.42	     16: evalabcbb5in -> evalabcstop : [], cost: 1
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Removed unreachable and leaf rules:
5.28/2.42	
5.28/2.42	   Start location: evalabcstart
5.28/2.42	
5.28/2.42	      0: evalabcstart -> evalabcbb0in : [], cost: 1
5.28/2.42	
5.28/2.42	      1: evalabcbb0in -> evalabc0 : [], cost: 1
5.28/2.42	
5.28/2.42	      2: evalabc0 -> evalabc1 : [], cost: 1
5.28/2.42	
5.28/2.42	      3: evalabc1 -> evalabc2 : [], cost: 1
5.28/2.42	
5.28/2.42	      4: evalabc2 -> evalabc3 : [], cost: 1
5.28/2.42	
5.28/2.42	      5: evalabc3 -> evalabc4 : [], cost: 1
5.28/2.42	
5.28/2.42	      6: evalabc4 -> evalabc5 : [], cost: 1
5.28/2.42	
5.28/2.42	      7: evalabc5 -> evalabcbb1in : A'=1, [], cost: 1
5.28/2.42	
5.28/2.42	      8: evalabcbb1in -> evalabcbb2in : C'=1, [ B>=A ], cost: 1
5.28/2.42	
5.28/2.42	     10: evalabcbb2in -> evalabcbb3in : [ D>=C ], cost: 1
5.28/2.42	
5.28/2.42	     11: evalabcbb2in -> evalabcbb4in : [ C>=1+D ], cost: 1
5.28/2.42	
5.28/2.42	     12: evalabcbb3in -> evalabcbb2in : C'=1+C, [], cost: 1
5.28/2.42	
5.28/2.42	     13: evalabcbb4in -> evalabc9 : E'=1+A, [], cost: 1
5.28/2.42	
5.28/2.42	     14: evalabc9 -> evalabc10 : [], cost: 1
5.28/2.42	
5.28/2.42	     15: evalabc10 -> evalabcbb1in : A'=E, [], cost: 1
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	### Simplification by acceleration and chaining ###
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Eliminated locations (on linear paths):
5.28/2.42	
5.28/2.42	   Start location: evalabcstart
5.28/2.42	
5.28/2.42	     23: evalabcstart -> evalabcbb1in : A'=1, [], cost: 8
5.28/2.42	
5.28/2.42	      8: evalabcbb1in -> evalabcbb2in : C'=1, [ B>=A ], cost: 1
5.28/2.42	
5.28/2.42	     24: evalabcbb2in -> evalabcbb2in : C'=1+C, [ D>=C ], cost: 2
5.28/2.42	
5.28/2.42	     27: evalabcbb2in -> evalabcbb1in : A'=1+A, E'=1+A, [ C>=1+D ], cost: 4
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Accelerating simple loops of location 9.
5.28/2.42	
5.28/2.42	   Accelerating the following rules:
5.28/2.42	
5.28/2.42	     24: evalabcbb2in -> evalabcbb2in : C'=1+C, [ D>=C ], cost: 2
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	   Accelerated rule 24 with metering function 1-C+D, yielding the new rule 28.
5.28/2.42	
5.28/2.42	   Removing the simple loops: 24.
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Accelerated all simple loops using metering functions (where possible):
5.28/2.42	
5.28/2.42	   Start location: evalabcstart
5.28/2.42	
5.28/2.42	     23: evalabcstart -> evalabcbb1in : A'=1, [], cost: 8
5.28/2.42	
5.28/2.42	      8: evalabcbb1in -> evalabcbb2in : C'=1, [ B>=A ], cost: 1
5.28/2.42	
5.28/2.42	     27: evalabcbb2in -> evalabcbb1in : A'=1+A, E'=1+A, [ C>=1+D ], cost: 4
5.28/2.42	
5.28/2.42	     28: evalabcbb2in -> evalabcbb2in : C'=1+D, [ D>=C ], cost: 2-2*C+2*D
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Chained accelerated rules (with incoming rules):
5.28/2.42	
5.28/2.42	   Start location: evalabcstart
5.28/2.42	
5.28/2.42	     23: evalabcstart -> evalabcbb1in : A'=1, [], cost: 8
5.28/2.42	
5.28/2.42	      8: evalabcbb1in -> evalabcbb2in : C'=1, [ B>=A ], cost: 1
5.28/2.42	
5.28/2.42	     29: evalabcbb1in -> evalabcbb2in : C'=1+D, [ B>=A && D>=1 ], cost: 1+2*D
5.28/2.42	
5.28/2.42	     27: evalabcbb2in -> evalabcbb1in : A'=1+A, E'=1+A, [ C>=1+D ], cost: 4
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Eliminated locations (on tree-shaped paths):
5.28/2.42	
5.28/2.42	   Start location: evalabcstart
5.28/2.42	
5.28/2.42	     23: evalabcstart -> evalabcbb1in : A'=1, [], cost: 8
5.28/2.42	
5.28/2.42	     30: evalabcbb1in -> evalabcbb1in : A'=1+A, C'=1, E'=1+A, [ B>=A && 1>=1+D ], cost: 5
5.28/2.42	
5.28/2.42	     31: evalabcbb1in -> evalabcbb1in : A'=1+A, C'=1+D, E'=1+A, [ B>=A && D>=1 ], cost: 5+2*D
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Accelerating simple loops of location 8.
5.28/2.42	
5.28/2.42	   Accelerating the following rules:
5.28/2.42	
5.28/2.42	     30: evalabcbb1in -> evalabcbb1in : A'=1+A, C'=1, E'=1+A, [ B>=A && 1>=1+D ], cost: 5
5.28/2.42	
5.28/2.42	     31: evalabcbb1in -> evalabcbb1in : A'=1+A, C'=1+D, E'=1+A, [ B>=A && D>=1 ], cost: 5+2*D
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	   Accelerated rule 30 with metering function 1-A+B, yielding the new rule 32.
5.28/2.42	
5.28/2.42	   Accelerated rule 31 with metering function 1-A+B, yielding the new rule 33.
5.28/2.42	
5.28/2.42	   Removing the simple loops: 30 31.
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Accelerated all simple loops using metering functions (where possible):
5.28/2.42	
5.28/2.42	   Start location: evalabcstart
5.28/2.42	
5.28/2.42	     23: evalabcstart -> evalabcbb1in : A'=1, [], cost: 8
5.28/2.42	
5.28/2.42	     32: evalabcbb1in -> evalabcbb1in : A'=1+B, C'=1, E'=1+B, [ B>=A && 1>=1+D ], cost: 5-5*A+5*B
5.28/2.42	
5.28/2.42	     33: evalabcbb1in -> evalabcbb1in : A'=1+B, C'=1+D, E'=1+B, [ B>=A && D>=1 ], cost: 5-2*(-1+A-B)*D-5*A+5*B
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Chained accelerated rules (with incoming rules):
5.28/2.42	
5.28/2.42	   Start location: evalabcstart
5.28/2.42	
5.28/2.42	     23: evalabcstart -> evalabcbb1in : A'=1, [], cost: 8
5.28/2.42	
5.28/2.42	     34: evalabcstart -> evalabcbb1in : A'=1+B, C'=1, E'=1+B, [ B>=1 && 1>=1+D ], cost: 8+5*B
5.28/2.42	
5.28/2.42	     35: evalabcstart -> evalabcbb1in : A'=1+B, C'=1+D, E'=1+B, [ B>=1 && D>=1 ], cost: 8+2*D*B+5*B
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Removed unreachable locations (and leaf rules with constant cost):
5.28/2.42	
5.28/2.42	   Start location: evalabcstart
5.28/2.42	
5.28/2.42	     34: evalabcstart -> evalabcbb1in : A'=1+B, C'=1, E'=1+B, [ B>=1 && 1>=1+D ], cost: 8+5*B
5.28/2.42	
5.28/2.42	     35: evalabcstart -> evalabcbb1in : A'=1+B, C'=1+D, E'=1+B, [ B>=1 && D>=1 ], cost: 8+2*D*B+5*B
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	### Computing asymptotic complexity ###
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Fully simplified ITS problem
5.28/2.42	
5.28/2.42	   Start location: evalabcstart
5.28/2.42	
5.28/2.42	     34: evalabcstart -> evalabcbb1in : A'=1+B, C'=1, E'=1+B, [ B>=1 && 1>=1+D ], cost: 8+5*B
5.28/2.42	
5.28/2.42	     35: evalabcstart -> evalabcbb1in : A'=1+B, C'=1+D, E'=1+B, [ B>=1 && D>=1 ], cost: 8+2*D*B+5*B
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Computing asymptotic complexity for rule 34
5.28/2.42	
5.28/2.42	   Solved the limit problem by the following transformations:
5.28/2.42	
5.28/2.42	      Created initial limit problem:
5.28/2.42	
5.28/2.42	      1-D (+/+!), B (+/+!), 8+5*B (+) [not solved]
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	      removing all constraints (solved by SMT)
5.28/2.42	
5.28/2.42	      resulting limit problem: [solved]
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	      applying transformation rule (C) using substitution {D==0,B==n}
5.28/2.42	
5.28/2.42	      resulting limit problem:
5.28/2.42	
5.28/2.42	      [solved]
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	   Solution:
5.28/2.42	
5.28/2.42	      D / 0
5.28/2.42	
5.28/2.42	      B / n
5.28/2.42	
5.28/2.42	   Resulting cost 8+5*n has complexity: Poly(n^1)
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Found new complexity Poly(n^1).
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Computing asymptotic complexity for rule 35
5.28/2.42	
5.28/2.42	   Solved the limit problem by the following transformations:
5.28/2.42	
5.28/2.42	      Created initial limit problem:
5.28/2.42	
5.28/2.42	      D (+/+!), 8+2*D*B+5*B (+), B (+/+!) [not solved]
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	      removing all constraints (solved by SMT)
5.28/2.42	
5.28/2.42	      resulting limit problem: [solved]
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	      applying transformation rule (C) using substitution {D==n,B==n}
5.28/2.42	
5.28/2.42	      resulting limit problem:
5.28/2.42	
5.28/2.42	      [solved]
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	   Solution:
5.28/2.42	
5.28/2.42	      D / n
5.28/2.42	
5.28/2.42	      B / n
5.28/2.42	
5.28/2.42	   Resulting cost 8+5*n+2*n^2 has complexity: Poly(n^2)
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Found new complexity Poly(n^2).
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	Obtained the following overall complexity (w.r.t. the length of the input n):
5.28/2.42	
5.28/2.42	   Complexity:  Poly(n^2)
5.28/2.42	
5.28/2.42	   Cpx degree:  2
5.28/2.42	
5.28/2.42	   Solved cost: 8+5*n+2*n^2
5.28/2.42	
5.28/2.42	   Rule cost:   8+2*D*B+5*B
5.28/2.42	
5.28/2.42	   Rule guard:  [ B>=1 && D>=1 ]
5.28/2.42	
5.28/2.42	
5.28/2.42	
5.28/2.42	WORST_CASE(Omega(n^2),?)
5.28/2.42	
5.28/2.42	
5.28/2.42	----------------------------------------
5.28/2.42	
5.28/2.42	(4)
5.28/2.42	BOUNDS(n^2, INF)
5.28/2.45	EOF