5.70/2.71	WORST_CASE(Omega(n^2), O(n^2))
5.70/2.72	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.70/2.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.70/2.72	
5.70/2.72	
5.70/2.72	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).
5.70/2.72	
5.70/2.72	(0) CpxIntTrs
5.70/2.72	(1) Koat Proof [FINISHED, 316 ms]
5.70/2.72	(2) BOUNDS(1, n^2)
5.70/2.72	(3) Loat Proof [FINISHED, 930 ms]
5.70/2.72	(4) BOUNDS(n^2, INF)
5.70/2.72	
5.70/2.72	
5.70/2.72	----------------------------------------
5.70/2.72	
5.70/2.72	(0)
5.70/2.72	Obligation:
5.70/2.72	Complexity Int TRS consisting of the following rules:
5.70/2.72	eval_speedSimpleMultipleDep_start(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultipleDep_bb0_in(v_m, v_n, v_x_0, v_y_0)) :|: TRUE
5.70/2.72	eval_speedSimpleMultipleDep_bb0_in(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultipleDep_0(v_m, v_n, v_x_0, v_y_0)) :|: TRUE
5.70/2.72	eval_speedSimpleMultipleDep_0(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultipleDep_1(v_m, v_n, v_x_0, v_y_0)) :|: TRUE
5.70/2.72	eval_speedSimpleMultipleDep_1(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultipleDep_2(v_m, v_n, v_x_0, v_y_0)) :|: TRUE
5.70/2.72	eval_speedSimpleMultipleDep_2(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultipleDep_3(v_m, v_n, v_x_0, v_y_0)) :|: TRUE
5.70/2.72	eval_speedSimpleMultipleDep_3(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultipleDep_4(v_m, v_n, v_x_0, v_y_0)) :|: TRUE
5.70/2.72	eval_speedSimpleMultipleDep_4(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultipleDep_5(v_m, v_n, v_x_0, v_y_0)) :|: TRUE
5.70/2.72	eval_speedSimpleMultipleDep_5(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultipleDep_6(v_m, v_n, v_x_0, v_y_0)) :|: TRUE
5.70/2.72	eval_speedSimpleMultipleDep_6(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultipleDep_7(v_m, v_n, v_x_0, v_y_0)) :|: TRUE
5.70/2.72	eval_speedSimpleMultipleDep_7(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(v_m, v_n, 0, 0)) :|: TRUE
5.70/2.72	eval_speedSimpleMultipleDep_bb1_in(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultipleDep_bb2_in(v_m, v_n, v_x_0, v_y_0)) :|: v_x_0 < v_n
5.70/2.72	eval_speedSimpleMultipleDep_bb1_in(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultipleDep_bb3_in(v_m, v_n, v_x_0, v_y_0)) :|: v_x_0 >= v_n
5.70/2.72	eval_speedSimpleMultipleDep_bb2_in(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(v_m, v_n, v_x_0, v_y_0 + 1)) :|: v_y_0 < v_m
5.70/2.72	eval_speedSimpleMultipleDep_bb2_in(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(v_m, v_n, v_x_0 + 1, v_y_0 + 1)) :|: v_y_0 < v_m && v_y_0 >= v_m
5.70/2.72	eval_speedSimpleMultipleDep_bb2_in(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(v_m, v_n, v_x_0, 0)) :|: v_y_0 >= v_m && v_y_0 < v_m
5.70/2.72	eval_speedSimpleMultipleDep_bb2_in(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(v_m, v_n, v_x_0 + 1, 0)) :|: v_y_0 >= v_m
5.70/2.72	eval_speedSimpleMultipleDep_bb3_in(v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedSimpleMultipleDep_stop(v_m, v_n, v_x_0, v_y_0)) :|: TRUE
5.70/2.72	
5.70/2.72	The start-symbols are:[eval_speedSimpleMultipleDep_start_4]
5.70/2.72	
5.70/2.72	
5.70/2.72	----------------------------------------
5.70/2.72	
5.70/2.72	(1) Koat Proof (FINISHED)
5.70/2.72	YES(?, 2*ar_2 + 2*ar_2*ar_3 + 2*ar_3 + 15)
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Initial complexity problem:
5.70/2.72	
5.70/2.72	1:	T:
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 /\ ar_1 >= ar_3 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, 0, ar_2, ar_3)) [ ar_1 >= ar_3 /\ ar_3 >= ar_1 + 1 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, 0, ar_2, ar_3)) [ ar_1 >= ar_3 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.70/2.72	
5.70/2.72		start location:	koat_start
5.70/2.72	
5.70/2.72		leaf cost:	0
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Testing for reachability in the complexity graph removes the following transitions from problem 1:
5.70/2.72	
5.70/2.72		evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 /\ ar_1 >= ar_3 ]
5.70/2.72	
5.70/2.72		evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, 0, ar_2, ar_3)) [ ar_1 >= ar_3 /\ ar_3 >= ar_1 + 1 ]
5.70/2.72	
5.70/2.72	We thus obtain the following problem:
5.70/2.72	
5.70/2.72	2:	T:
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, 0, ar_2, ar_3)) [ ar_1 >= ar_3 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.70/2.72	
5.70/2.72		start location:	koat_start
5.70/2.72	
5.70/2.72		leaf cost:	0
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Repeatedly propagating knowledge in problem 2 produces the following problem:
5.70/2.72	
5.70/2.72	3:	T:
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, 0, ar_2, ar_3)) [ ar_1 >= ar_3 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.70/2.72	
5.70/2.72		start location:	koat_start
5.70/2.72	
5.70/2.72		leaf cost:	0
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	A polynomial rank function with
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDepbb3in) = 1
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDepstop) = 0
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDepbb2in) = 2
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDepbb1in) = 2
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDep7) = 2
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDep6) = 2
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDep5) = 2
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDep4) = 2
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDep3) = 2
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDep2) = 2
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDep1) = 2
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDep0) = 2
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDepbb0in) = 2
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDepstart) = 2
5.70/2.72	
5.70/2.72		Pol(koat_start) = 2
5.70/2.72	
5.70/2.72	orients all transitions weakly and the transitions
5.70/2.72	
5.70/2.72		evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72		evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
5.70/2.72	
5.70/2.72	strictly and produces the following problem:
5.70/2.72	
5.70/2.72	4:	T:
5.70/2.72	
5.70/2.72			(Comp: 2, Cost: 1)    evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, 0, ar_2, ar_3)) [ ar_1 >= ar_3 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
5.70/2.72	
5.70/2.72			(Comp: 2, Cost: 1)    evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.70/2.72	
5.70/2.72		start location:	koat_start
5.70/2.72	
5.70/2.72		leaf cost:	0
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Applied AI with 'oct' on problem 4 to obtain the following invariants:
5.70/2.72	
5.70/2.72	  For symbol evalspeedSimpleMultipleDepbb1in: X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
5.70/2.72	
5.70/2.72	  For symbol evalspeedSimpleMultipleDepbb2in: X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
5.70/2.72	
5.70/2.72	  For symbol evalspeedSimpleMultipleDepbb3in: X_1 - X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	This yielded the following problem:
5.70/2.72	
5.70/2.72	5:	T:
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_0 + 1 ]
5.70/2.72	
5.70/2.72			(Comp: 2, Cost: 1)    evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_2 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_1 + 1 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, 0, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_3 ]
5.70/2.72	
5.70/2.72			(Comp: 2, Cost: 1)    evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
5.70/2.72	
5.70/2.72		start location:	koat_start
5.70/2.72	
5.70/2.72		leaf cost:	0
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	A polynomial rank function with
5.70/2.72	
5.70/2.72		Pol(koat_start) = V_3
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDepstart) = V_3
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDepbb0in) = V_3
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDep0) = V_3
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDep1) = V_3
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDep2) = V_3
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDep3) = V_3
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDep4) = V_3
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDep5) = V_3
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDep6) = V_3
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDep7) = V_3
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDepbb1in) = -V_1 + V_3
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDepbb2in) = -V_1 + V_3
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDepbb3in) = -V_1 + V_3
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDepstop) = -V_1 + V_3
5.70/2.72	
5.70/2.72	orients all transitions weakly and the transition
5.70/2.72	
5.70/2.72		evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, 0, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_3 ]
5.70/2.72	
5.70/2.72	strictly and produces the following problem:
5.70/2.72	
5.70/2.72	6:	T:
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)       evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)       evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)       evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)       evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)       evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)       evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)       evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)       evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)       evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)       evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)       evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_0 + 1 ]
5.70/2.72	
5.70/2.72			(Comp: 2, Cost: 1)       evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_2 ]
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)       evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_1 + 1 ]
5.70/2.72	
5.70/2.72			(Comp: ar_2, Cost: 1)    evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, 0, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_3 ]
5.70/2.72	
5.70/2.72			(Comp: 2, Cost: 1)       evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
5.70/2.72	
5.70/2.72		start location:	koat_start
5.70/2.72	
5.70/2.72		leaf cost:	0
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	A polynomial rank function with
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDepbb2in) = -V_2 + V_4
5.70/2.72	
5.70/2.72		Pol(evalspeedSimpleMultipleDepbb1in) = -V_2 + V_4
5.70/2.72	
5.70/2.72	and size complexities
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-0) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-1) = 0
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-2) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-3) = ar_3
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, 0, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_3 ]", 0-0) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, 0, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_3 ]", 0-1) = 0
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, 0, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_3 ]", 0-2) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, 0, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_3 ]", 0-3) = ar_3
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_3 >= ar_1 + 1 ]", 0-0) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_3 >= ar_1 + 1 ]", 0-1) = ar_3
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_3 >= ar_1 + 1 ]", 0-2) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_3 >= ar_1 + 1 ]", 0-3) = ar_3
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_2 ]", 0-0) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_2 ]", 0-1) = 0
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_2 ]", 0-2) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_2 ]", 0-3) = ar_3
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= ar_0 + 1 ]", 0-0) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= ar_0 + 1 ]", 0-1) = ar_3
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= ar_0 + 1 ]", 0-2) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= ar_0 + 1 ]", 0-3) = ar_3
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))", 0-0) = 0
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))", 0-1) = 0
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))", 0-2) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))", 0-3) = ar_3
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.70/2.72	
5.70/2.72		S("evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.70/2.72	
5.70/2.72		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
5.70/2.72	
5.70/2.72		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
5.70/2.72	
5.70/2.72		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
5.70/2.72	
5.70/2.72		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
5.70/2.72	
5.70/2.72	orients the transitions
5.70/2.72	
5.70/2.72		evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_1 + 1 ]
5.70/2.72	
5.70/2.72		evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_0 + 1 ]
5.70/2.72	
5.70/2.72	weakly and the transition
5.70/2.72	
5.70/2.72		evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_1 + 1 ]
5.70/2.72	
5.70/2.72	strictly and produces the following problem:
5.70/2.72	
5.70/2.72	7:	T:
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 0)                   koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                   evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                   evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                   evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                   evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                   evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                   evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                   evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                   evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                   evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                   evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ?, Cost: 1)                   evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_0 + 1 ]
5.70/2.72	
5.70/2.72			(Comp: 2, Cost: 1)                   evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_2 ]
5.70/2.72	
5.70/2.72			(Comp: ar_2*ar_3 + ar_3, Cost: 1)    evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_1 + 1 ]
5.70/2.72	
5.70/2.72			(Comp: ar_2, Cost: 1)                evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, 0, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_3 ]
5.70/2.72	
5.70/2.72			(Comp: 2, Cost: 1)                   evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
5.70/2.72	
5.70/2.72		start location:	koat_start
5.70/2.72	
5.70/2.72		leaf cost:	0
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Repeatedly propagating knowledge in problem 7 produces the following problem:
5.70/2.72	
5.70/2.72	8:	T:
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 0)                              koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                              evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                              evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                              evalspeedSimpleMultipleDep0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                              evalspeedSimpleMultipleDep1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                              evalspeedSimpleMultipleDep2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                              evalspeedSimpleMultipleDep3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                              evalspeedSimpleMultipleDep4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                              evalspeedSimpleMultipleDep5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                              evalspeedSimpleMultipleDep6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: 1, Cost: 1)                              evalspeedSimpleMultipleDep7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))
5.70/2.72	
5.70/2.72			(Comp: ar_2 + ar_2*ar_3 + ar_3 + 1, Cost: 1)    evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_0 + 1 ]
5.70/2.72	
5.70/2.72			(Comp: 2, Cost: 1)                              evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_2 ]
5.70/2.72	
5.70/2.72			(Comp: ar_2*ar_3 + ar_3, Cost: 1)               evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_1 + 1 ]
5.70/2.72	
5.70/2.72			(Comp: ar_2, Cost: 1)                           evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, 0, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_3 ]
5.70/2.72	
5.70/2.72			(Comp: 2, Cost: 1)                              evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
5.70/2.72	
5.70/2.72		start location:	koat_start
5.70/2.72	
5.70/2.72		leaf cost:	0
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Complexity upper bound 2*ar_2 + 2*ar_2*ar_3 + 2*ar_3 + 15
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Time: 0.367 sec (SMT: 0.296 sec)
5.70/2.72	
5.70/2.72	
5.70/2.72	----------------------------------------
5.70/2.72	
5.70/2.72	(2)
5.70/2.72	BOUNDS(1, n^2)
5.70/2.72	
5.70/2.72	----------------------------------------
5.70/2.72	
5.70/2.72	(3) Loat Proof (FINISHED)
5.70/2.72	
5.70/2.72	
5.70/2.72	### Pre-processing the ITS problem ###
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Initial linear ITS problem
5.70/2.72	
5.70/2.72	   Start location: evalspeedSimpleMultipleDepstart
5.70/2.72	
5.70/2.72	      0: evalspeedSimpleMultipleDepstart -> evalspeedSimpleMultipleDepbb0in : [], cost: 1
5.70/2.72	
5.70/2.72	      1: evalspeedSimpleMultipleDepbb0in -> evalspeedSimpleMultipleDep0 : [], cost: 1
5.70/2.72	
5.70/2.72	      2: evalspeedSimpleMultipleDep0 -> evalspeedSimpleMultipleDep1 : [], cost: 1
5.70/2.72	
5.70/2.72	      3: evalspeedSimpleMultipleDep1 -> evalspeedSimpleMultipleDep2 : [], cost: 1
5.70/2.72	
5.70/2.72	      4: evalspeedSimpleMultipleDep2 -> evalspeedSimpleMultipleDep3 : [], cost: 1
5.70/2.72	
5.70/2.72	      5: evalspeedSimpleMultipleDep3 -> evalspeedSimpleMultipleDep4 : [], cost: 1
5.70/2.72	
5.70/2.72	      6: evalspeedSimpleMultipleDep4 -> evalspeedSimpleMultipleDep5 : [], cost: 1
5.70/2.72	
5.70/2.72	      7: evalspeedSimpleMultipleDep5 -> evalspeedSimpleMultipleDep6 : [], cost: 1
5.70/2.72	
5.70/2.72	      8: evalspeedSimpleMultipleDep6 -> evalspeedSimpleMultipleDep7 : [], cost: 1
5.70/2.72	
5.70/2.72	      9: evalspeedSimpleMultipleDep7 -> evalspeedSimpleMultipleDepbb1in : A'=0, B'=0, [], cost: 1
5.70/2.72	
5.70/2.72	     10: evalspeedSimpleMultipleDepbb1in -> evalspeedSimpleMultipleDepbb2in : [ C>=1+A ], cost: 1
5.70/2.72	
5.70/2.72	     11: evalspeedSimpleMultipleDepbb1in -> evalspeedSimpleMultipleDepbb3in : [ A>=C ], cost: 1
5.70/2.72	
5.70/2.72	     12: evalspeedSimpleMultipleDepbb2in -> evalspeedSimpleMultipleDepbb1in : B'=1+B, [ D>=1+B ], cost: 1
5.70/2.72	
5.70/2.72	     13: evalspeedSimpleMultipleDepbb2in -> evalspeedSimpleMultipleDepbb1in : A'=1+A, B'=1+B, [ D>=1+B && B>=D ], cost: 1
5.70/2.72	
5.70/2.72	     14: evalspeedSimpleMultipleDepbb2in -> evalspeedSimpleMultipleDepbb1in : B'=0, [ B>=D && D>=1+B ], cost: 1
5.70/2.72	
5.70/2.72	     15: evalspeedSimpleMultipleDepbb2in -> evalspeedSimpleMultipleDepbb1in : A'=1+A, B'=0, [ B>=D ], cost: 1
5.70/2.72	
5.70/2.72	     16: evalspeedSimpleMultipleDepbb3in -> evalspeedSimpleMultipleDepstop : [], cost: 1
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Removed unreachable and leaf rules:
5.70/2.72	
5.70/2.72	   Start location: evalspeedSimpleMultipleDepstart
5.70/2.72	
5.70/2.72	      0: evalspeedSimpleMultipleDepstart -> evalspeedSimpleMultipleDepbb0in : [], cost: 1
5.70/2.72	
5.70/2.72	      1: evalspeedSimpleMultipleDepbb0in -> evalspeedSimpleMultipleDep0 : [], cost: 1
5.70/2.72	
5.70/2.72	      2: evalspeedSimpleMultipleDep0 -> evalspeedSimpleMultipleDep1 : [], cost: 1
5.70/2.72	
5.70/2.72	      3: evalspeedSimpleMultipleDep1 -> evalspeedSimpleMultipleDep2 : [], cost: 1
5.70/2.72	
5.70/2.72	      4: evalspeedSimpleMultipleDep2 -> evalspeedSimpleMultipleDep3 : [], cost: 1
5.70/2.72	
5.70/2.72	      5: evalspeedSimpleMultipleDep3 -> evalspeedSimpleMultipleDep4 : [], cost: 1
5.70/2.72	
5.70/2.72	      6: evalspeedSimpleMultipleDep4 -> evalspeedSimpleMultipleDep5 : [], cost: 1
5.70/2.72	
5.70/2.72	      7: evalspeedSimpleMultipleDep5 -> evalspeedSimpleMultipleDep6 : [], cost: 1
5.70/2.72	
5.70/2.72	      8: evalspeedSimpleMultipleDep6 -> evalspeedSimpleMultipleDep7 : [], cost: 1
5.70/2.72	
5.70/2.72	      9: evalspeedSimpleMultipleDep7 -> evalspeedSimpleMultipleDepbb1in : A'=0, B'=0, [], cost: 1
5.70/2.72	
5.70/2.72	     10: evalspeedSimpleMultipleDepbb1in -> evalspeedSimpleMultipleDepbb2in : [ C>=1+A ], cost: 1
5.70/2.72	
5.70/2.72	     12: evalspeedSimpleMultipleDepbb2in -> evalspeedSimpleMultipleDepbb1in : B'=1+B, [ D>=1+B ], cost: 1
5.70/2.72	
5.70/2.72	     13: evalspeedSimpleMultipleDepbb2in -> evalspeedSimpleMultipleDepbb1in : A'=1+A, B'=1+B, [ D>=1+B && B>=D ], cost: 1
5.70/2.72	
5.70/2.72	     14: evalspeedSimpleMultipleDepbb2in -> evalspeedSimpleMultipleDepbb1in : B'=0, [ B>=D && D>=1+B ], cost: 1
5.70/2.72	
5.70/2.72	     15: evalspeedSimpleMultipleDepbb2in -> evalspeedSimpleMultipleDepbb1in : A'=1+A, B'=0, [ B>=D ], cost: 1
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Removed rules with unsatisfiable guard:
5.70/2.72	
5.70/2.72	   Start location: evalspeedSimpleMultipleDepstart
5.70/2.72	
5.70/2.72	      0: evalspeedSimpleMultipleDepstart -> evalspeedSimpleMultipleDepbb0in : [], cost: 1
5.70/2.72	
5.70/2.72	      1: evalspeedSimpleMultipleDepbb0in -> evalspeedSimpleMultipleDep0 : [], cost: 1
5.70/2.72	
5.70/2.72	      2: evalspeedSimpleMultipleDep0 -> evalspeedSimpleMultipleDep1 : [], cost: 1
5.70/2.72	
5.70/2.72	      3: evalspeedSimpleMultipleDep1 -> evalspeedSimpleMultipleDep2 : [], cost: 1
5.70/2.72	
5.70/2.72	      4: evalspeedSimpleMultipleDep2 -> evalspeedSimpleMultipleDep3 : [], cost: 1
5.70/2.72	
5.70/2.72	      5: evalspeedSimpleMultipleDep3 -> evalspeedSimpleMultipleDep4 : [], cost: 1
5.70/2.72	
5.70/2.72	      6: evalspeedSimpleMultipleDep4 -> evalspeedSimpleMultipleDep5 : [], cost: 1
5.70/2.72	
5.70/2.72	      7: evalspeedSimpleMultipleDep5 -> evalspeedSimpleMultipleDep6 : [], cost: 1
5.70/2.72	
5.70/2.72	      8: evalspeedSimpleMultipleDep6 -> evalspeedSimpleMultipleDep7 : [], cost: 1
5.70/2.72	
5.70/2.72	      9: evalspeedSimpleMultipleDep7 -> evalspeedSimpleMultipleDepbb1in : A'=0, B'=0, [], cost: 1
5.70/2.72	
5.70/2.72	     10: evalspeedSimpleMultipleDepbb1in -> evalspeedSimpleMultipleDepbb2in : [ C>=1+A ], cost: 1
5.70/2.72	
5.70/2.72	     12: evalspeedSimpleMultipleDepbb2in -> evalspeedSimpleMultipleDepbb1in : B'=1+B, [ D>=1+B ], cost: 1
5.70/2.72	
5.70/2.72	     15: evalspeedSimpleMultipleDepbb2in -> evalspeedSimpleMultipleDepbb1in : A'=1+A, B'=0, [ B>=D ], cost: 1
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	### Simplification by acceleration and chaining ###
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Eliminated locations (on linear paths):
5.70/2.72	
5.70/2.72	   Start location: evalspeedSimpleMultipleDepstart
5.70/2.72	
5.70/2.72	     25: evalspeedSimpleMultipleDepstart -> evalspeedSimpleMultipleDepbb1in : A'=0, B'=0, [], cost: 10
5.70/2.72	
5.70/2.72	     10: evalspeedSimpleMultipleDepbb1in -> evalspeedSimpleMultipleDepbb2in : [ C>=1+A ], cost: 1
5.70/2.72	
5.70/2.72	     12: evalspeedSimpleMultipleDepbb2in -> evalspeedSimpleMultipleDepbb1in : B'=1+B, [ D>=1+B ], cost: 1
5.70/2.72	
5.70/2.72	     15: evalspeedSimpleMultipleDepbb2in -> evalspeedSimpleMultipleDepbb1in : A'=1+A, B'=0, [ B>=D ], cost: 1
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Eliminated locations (on tree-shaped paths):
5.70/2.72	
5.70/2.72	   Start location: evalspeedSimpleMultipleDepstart
5.70/2.72	
5.70/2.72	     25: evalspeedSimpleMultipleDepstart -> evalspeedSimpleMultipleDepbb1in : A'=0, B'=0, [], cost: 10
5.70/2.72	
5.70/2.72	     26: evalspeedSimpleMultipleDepbb1in -> evalspeedSimpleMultipleDepbb1in : B'=1+B, [ C>=1+A && D>=1+B ], cost: 2
5.70/2.72	
5.70/2.72	     27: evalspeedSimpleMultipleDepbb1in -> evalspeedSimpleMultipleDepbb1in : A'=1+A, B'=0, [ C>=1+A && B>=D ], cost: 2
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Accelerating simple loops of location 10.
5.70/2.72	
5.70/2.72	   Accelerating the following rules:
5.70/2.72	
5.70/2.72	     26: evalspeedSimpleMultipleDepbb1in -> evalspeedSimpleMultipleDepbb1in : B'=1+B, [ C>=1+A && D>=1+B ], cost: 2
5.70/2.72	
5.70/2.72	     27: evalspeedSimpleMultipleDepbb1in -> evalspeedSimpleMultipleDepbb1in : A'=1+A, B'=0, [ C>=1+A && B>=D ], cost: 2
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	   Accelerated rule 26 with metering function D-B, yielding the new rule 28.
5.70/2.72	
5.70/2.72	   Accelerated rule 27 with metering function C-A (after strengthening guard), yielding the new rule 29.
5.70/2.72	
5.70/2.72	   Nested simple loops 27 (outer loop) and 28 (inner loop) with metering function -1+C-A, resulting in the new rules: 30, 31.
5.70/2.72	
5.70/2.72	   Removing the simple loops: 26 27.
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Accelerated all simple loops using metering functions (where possible):
5.70/2.72	
5.70/2.72	   Start location: evalspeedSimpleMultipleDepstart
5.70/2.72	
5.70/2.72	     25: evalspeedSimpleMultipleDepstart -> evalspeedSimpleMultipleDepbb1in : A'=0, B'=0, [], cost: 10
5.70/2.72	
5.70/2.72	     28: evalspeedSimpleMultipleDepbb1in -> evalspeedSimpleMultipleDepbb1in : B'=D, [ C>=1+A && D>=1+B ], cost: 2*D-2*B
5.70/2.72	
5.70/2.72	     29: evalspeedSimpleMultipleDepbb1in -> evalspeedSimpleMultipleDepbb1in : A'=C, B'=0, [ C>=1+A && B>=D && 0>=D ], cost: 2*C-2*A
5.70/2.72	
5.70/2.72	     30: evalspeedSimpleMultipleDepbb1in -> evalspeedSimpleMultipleDepbb1in : A'=-1+C, B'=D, [ B>=D && C>=2+A && D>=1 ], cost: -2+2*C+2*(-1+C-A)*D-2*A
5.70/2.72	
5.70/2.72	     31: evalspeedSimpleMultipleDepbb1in -> evalspeedSimpleMultipleDepbb1in : A'=-1+C, B'=D, [ D>=1+B && C>=2+A && D>=1 ], cost: -2+2*C+2*(-1+C-A)*D+2*D-2*A-2*B
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Chained accelerated rules (with incoming rules):
5.70/2.72	
5.70/2.72	   Start location: evalspeedSimpleMultipleDepstart
5.70/2.72	
5.70/2.72	     25: evalspeedSimpleMultipleDepstart -> evalspeedSimpleMultipleDepbb1in : A'=0, B'=0, [], cost: 10
5.70/2.72	
5.70/2.72	     32: evalspeedSimpleMultipleDepstart -> evalspeedSimpleMultipleDepbb1in : A'=0, B'=D, [ C>=1 && D>=1 ], cost: 10+2*D
5.70/2.72	
5.70/2.72	     33: evalspeedSimpleMultipleDepstart -> evalspeedSimpleMultipleDepbb1in : A'=C, B'=0, [ C>=1 && 0>=D ], cost: 10+2*C
5.70/2.72	
5.70/2.72	     34: evalspeedSimpleMultipleDepstart -> evalspeedSimpleMultipleDepbb1in : A'=-1+C, B'=D, [ D>=1 && C>=2 ], cost: 8+2*D*(-1+C)+2*C+2*D
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Removed unreachable locations (and leaf rules with constant cost):
5.70/2.72	
5.70/2.72	   Start location: evalspeedSimpleMultipleDepstart
5.70/2.72	
5.70/2.72	     32: evalspeedSimpleMultipleDepstart -> evalspeedSimpleMultipleDepbb1in : A'=0, B'=D, [ C>=1 && D>=1 ], cost: 10+2*D
5.70/2.72	
5.70/2.72	     33: evalspeedSimpleMultipleDepstart -> evalspeedSimpleMultipleDepbb1in : A'=C, B'=0, [ C>=1 && 0>=D ], cost: 10+2*C
5.70/2.72	
5.70/2.72	     34: evalspeedSimpleMultipleDepstart -> evalspeedSimpleMultipleDepbb1in : A'=-1+C, B'=D, [ D>=1 && C>=2 ], cost: 8+2*D*(-1+C)+2*C+2*D
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	### Computing asymptotic complexity ###
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Fully simplified ITS problem
5.70/2.72	
5.70/2.72	   Start location: evalspeedSimpleMultipleDepstart
5.70/2.72	
5.70/2.72	     32: evalspeedSimpleMultipleDepstart -> evalspeedSimpleMultipleDepbb1in : A'=0, B'=D, [ C>=1 && D>=1 ], cost: 10+2*D
5.70/2.72	
5.70/2.72	     33: evalspeedSimpleMultipleDepstart -> evalspeedSimpleMultipleDepbb1in : A'=C, B'=0, [ C>=1 && 0>=D ], cost: 10+2*C
5.70/2.72	
5.70/2.72	     34: evalspeedSimpleMultipleDepstart -> evalspeedSimpleMultipleDepbb1in : A'=-1+C, B'=D, [ D>=1 && C>=2 ], cost: 8+2*D*(-1+C)+2*C+2*D
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Computing asymptotic complexity for rule 32
5.70/2.72	
5.70/2.72	   Solved the limit problem by the following transformations:
5.70/2.72	
5.70/2.72	      Created initial limit problem:
5.70/2.72	
5.70/2.72	      10+2*D (+), C (+/+!), D (+/+!) [not solved]
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	      removing all constraints (solved by SMT)
5.70/2.72	
5.70/2.72	      resulting limit problem: [solved]
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	      applying transformation rule (C) using substitution {C==n,D==n}
5.70/2.72	
5.70/2.72	      resulting limit problem:
5.70/2.72	
5.70/2.72	      [solved]
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	   Solution:
5.70/2.72	
5.70/2.72	      C / n
5.70/2.72	
5.70/2.72	      D / n
5.70/2.72	
5.70/2.72	   Resulting cost 10+2*n has complexity: Poly(n^1)
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Found new complexity Poly(n^1).
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Computing asymptotic complexity for rule 34
5.70/2.72	
5.70/2.72	   Solved the limit problem by the following transformations:
5.70/2.72	
5.70/2.72	      Created initial limit problem:
5.70/2.72	
5.70/2.72	      D (+/+!), -1+C (+/+!), 8+2*C+2*C*D (+) [not solved]
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	      removing all constraints (solved by SMT)
5.70/2.72	
5.70/2.72	      resulting limit problem: [solved]
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	      applying transformation rule (C) using substitution {C==n,D==n}
5.70/2.72	
5.70/2.72	      resulting limit problem:
5.70/2.72	
5.70/2.72	      [solved]
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	   Solution:
5.70/2.72	
5.70/2.72	      C / n
5.70/2.72	
5.70/2.72	      D / n
5.70/2.72	
5.70/2.72	   Resulting cost 8+2*n^2+2*n has complexity: Poly(n^2)
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Found new complexity Poly(n^2).
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	Obtained the following overall complexity (w.r.t. the length of the input n):
5.70/2.72	
5.70/2.72	   Complexity:  Poly(n^2)
5.70/2.72	
5.70/2.72	   Cpx degree:  2
5.70/2.72	
5.70/2.72	   Solved cost: 8+2*n^2+2*n
5.70/2.72	
5.70/2.72	   Rule cost:   8+2*D*(-1+C)+2*C+2*D
5.70/2.72	
5.70/2.72	   Rule guard:  [ D>=1 && C>=2 ]
5.70/2.72	
5.70/2.72	
5.70/2.72	
5.70/2.72	WORST_CASE(Omega(n^2),?)
5.70/2.72	
5.70/2.72	
5.70/2.72	----------------------------------------
5.70/2.72	
5.70/2.72	(4)
5.70/2.72	BOUNDS(n^2, INF)
5.85/2.75	EOF