2.20/1.31	WORST_CASE(?, O(n^2))
2.20/1.32	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.20/1.32	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.20/1.32	
2.20/1.32	
2.20/1.32	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.20/1.32	
2.20/1.32	(0) CpxIntTrs
2.20/1.32	(1) Koat Proof [FINISHED, 83 ms]
2.20/1.32	(2) BOUNDS(1, n^2)
2.20/1.32	
2.20/1.32	
2.20/1.32	----------------------------------------
2.20/1.32	
2.20/1.32	(0)
2.20/1.32	Obligation:
2.20/1.32	Complexity Int TRS consisting of the following rules:
2.20/1.32	eval_speedNestedMultipleDep_start(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb0_in(v_1, v_m, v_n, v_x.0, v_y.0)) :|: TRUE
2.20/1.32	eval_speedNestedMultipleDep_bb0_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb1_in(v_1, v_m, v_n, 0, v_y.0)) :|: TRUE
2.20/1.32	eval_speedNestedMultipleDep_bb1_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb2_in(v_1, v_m, v_n, v_x.0, v_y.0)) :|: v_x.0 < v_n
2.20/1.32	eval_speedNestedMultipleDep_bb1_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb5_in(v_1, v_m, v_n, v_x.0, v_y.0)) :|: v_x.0 >= v_n
2.20/1.32	eval_speedNestedMultipleDep_bb2_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb3_in(v_x.0 + 1, v_m, v_n, v_x.0, 0)) :|: TRUE
2.20/1.32	eval_speedNestedMultipleDep_bb3_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb4_in(v_1, v_m, v_n, v_x.0, v_y.0)) :|: v_y.0 < v_m
2.20/1.32	eval_speedNestedMultipleDep_bb3_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb1_in(v_1, v_m, v_n, v_1, v_y.0)) :|: v_y.0 >= v_m
2.20/1.32	eval_speedNestedMultipleDep_bb4_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb3_in(v_1, v_m, v_n, v_x.0, v_y.0 + 1)) :|: TRUE
2.20/1.32	eval_speedNestedMultipleDep_bb5_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_stop(v_1, v_m, v_n, v_x.0, v_y.0)) :|: TRUE
2.20/1.32	
2.20/1.32	The start-symbols are:[eval_speedNestedMultipleDep_start_5]
2.20/1.32	
2.20/1.32	
2.20/1.32	----------------------------------------
2.20/1.32	
2.20/1.32	(1) Koat Proof (FINISHED)
2.20/1.32	YES(?, 3*ar_1 + 2*ar_1*ar_4 + 6)
2.20/1.32	
2.20/1.32	
2.20/1.32	
2.20/1.32	Initial complexity problem:
2.20/1.32	
2.20/1.32	1:	T:
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.20/1.32	
2.20/1.32		start location:	koat_start
2.20/1.32	
2.20/1.32		leaf cost:	0
2.20/1.32	
2.20/1.32	
2.20/1.32	
2.20/1.32	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.20/1.32	
2.20/1.32	2:	T:
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 1)    evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 1)    evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.20/1.32	
2.20/1.32		start location:	koat_start
2.20/1.32	
2.20/1.32		leaf cost:	0
2.20/1.32	
2.20/1.32	
2.20/1.32	
2.20/1.32	A polynomial rank function with
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepstart) = 2
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepbb0in) = 2
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepbb1in) = 2
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepbb2in) = 2
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepbb5in) = 1
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepbb3in) = 2
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepbb4in) = 2
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepstop) = 0
2.20/1.32	
2.20/1.32		Pol(koat_start) = 2
2.20/1.32	
2.20/1.32	orients all transitions weakly and the transitions
2.20/1.32	
2.20/1.32		evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32		evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
2.20/1.32	
2.20/1.32	strictly and produces the following problem:
2.20/1.32	
2.20/1.32	3:	T:
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 1)    evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 1)    evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
2.20/1.32	
2.20/1.32			(Comp: 2, Cost: 1)    evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)    evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 2, Cost: 1)    evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.20/1.32	
2.20/1.32		start location:	koat_start
2.20/1.32	
2.20/1.32		leaf cost:	0
2.20/1.32	
2.20/1.32	
2.20/1.32	
2.20/1.32	A polynomial rank function with
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepstart) = V_2
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepbb0in) = V_2
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepbb1in) = -V_1 + V_2
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepbb2in) = -V_1 + V_2 - 1
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepbb5in) = -V_1 + V_2
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepbb3in) = V_2 - V_3
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepbb4in) = V_2 - V_3
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepstop) = -V_1 + V_2
2.20/1.32	
2.20/1.32		Pol(koat_start) = V_2
2.20/1.32	
2.20/1.32	orients all transitions weakly and the transition
2.20/1.32	
2.20/1.32		evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
2.20/1.32	
2.20/1.32	strictly and produces the following problem:
2.20/1.32	
2.20/1.32	4:	T:
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 1)       evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 1)       evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ar_1, Cost: 1)    evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
2.20/1.32	
2.20/1.32			(Comp: 2, Cost: 1)       evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)       evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)       evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)       evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)       evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 2, Cost: 1)       evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.20/1.32	
2.20/1.32		start location:	koat_start
2.20/1.32	
2.20/1.32		leaf cost:	0
2.20/1.32	
2.20/1.32	
2.20/1.32	
2.20/1.32	Repeatedly propagating knowledge in problem 4 produces the following problem:
2.20/1.32	
2.20/1.32	5:	T:
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 1)       evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 1)       evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ar_1, Cost: 1)    evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
2.20/1.32	
2.20/1.32			(Comp: 2, Cost: 1)       evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
2.20/1.32	
2.20/1.32			(Comp: ar_1, Cost: 1)    evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)       evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)       evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)       evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 2, Cost: 1)       evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.20/1.32	
2.20/1.32		start location:	koat_start
2.20/1.32	
2.20/1.32		leaf cost:	0
2.20/1.32	
2.20/1.32	
2.20/1.32	
2.20/1.32	A polynomial rank function with
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepbb4in) = 1
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepbb3in) = 1
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepbb1in) = 0
2.20/1.32	
2.20/1.32	and size complexities
2.20/1.32	
2.20/1.32		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0
2.20/1.32	
2.20/1.32		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2
2.20/1.32	
2.20/1.32		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3
2.20/1.32	
2.20/1.32		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_1 + ar_2
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ?
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-0) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-2) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-3) = ?
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-0) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-2) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-3) = ?
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-0) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-2) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-3) = ?
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-0) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-2) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-3) = 0
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-0) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-2) = ar_1 + ar_2
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-3) = ?
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-0) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-2) = ar_1 + ar_2
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-3) = ?
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))", 0-0) = 0
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
2.20/1.32	
2.20/1.32	orients the transitions
2.20/1.32	
2.20/1.32		evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
2.20/1.32	
2.20/1.32		evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
2.20/1.32	
2.20/1.32		evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
2.20/1.32	
2.20/1.32	weakly and the transition
2.20/1.32	
2.20/1.32		evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
2.20/1.32	
2.20/1.32	strictly and produces the following problem:
2.20/1.32	
2.20/1.32	6:	T:
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 1)       evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 1)       evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ar_1, Cost: 1)    evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
2.20/1.32	
2.20/1.32			(Comp: 2, Cost: 1)       evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
2.20/1.32	
2.20/1.32			(Comp: ar_1, Cost: 1)    evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)       evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
2.20/1.32	
2.20/1.32			(Comp: ar_1, Cost: 1)    evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)       evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 2, Cost: 1)       evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.20/1.32	
2.20/1.32		start location:	koat_start
2.20/1.32	
2.20/1.32		leaf cost:	0
2.20/1.32	
2.20/1.32	
2.20/1.32	
2.20/1.32	A polynomial rank function with
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepbb4in) = -V_4 + V_5 - 1
2.20/1.32	
2.20/1.32		Pol(evalspeedNestedMultipleDepbb3in) = -V_4 + V_5
2.20/1.32	
2.20/1.32	and size complexities
2.20/1.32	
2.20/1.32		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0
2.20/1.32	
2.20/1.32		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2
2.20/1.32	
2.20/1.32		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3
2.20/1.32	
2.20/1.32		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_1 + ar_2
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ?
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-0) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-2) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-3) = ?
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-0) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-2) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-3) = ?
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-0) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-2) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-3) = ?
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-0) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-2) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-3) = 0
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-0) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-2) = ar_1 + ar_2
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-3) = ?
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-0) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-2) = ar_1 + ar_2
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-3) = ?
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))", 0-0) = 0
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
2.20/1.32	
2.20/1.32		S("evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
2.20/1.32	
2.20/1.32	orients the transitions
2.20/1.32	
2.20/1.32		evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
2.20/1.32	
2.20/1.32		evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
2.20/1.32	
2.20/1.32	weakly and the transition
2.20/1.32	
2.20/1.32		evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
2.20/1.32	
2.20/1.32	strictly and produces the following problem:
2.20/1.32	
2.20/1.32	7:	T:
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 1)            evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 1)            evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ar_1, Cost: 1)         evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
2.20/1.32	
2.20/1.32			(Comp: 2, Cost: 1)            evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
2.20/1.32	
2.20/1.32			(Comp: ar_1, Cost: 1)         evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ar_1*ar_4, Cost: 1)    evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
2.20/1.32	
2.20/1.32			(Comp: ar_1, Cost: 1)         evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
2.20/1.32	
2.20/1.32			(Comp: ?, Cost: 1)            evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 2, Cost: 1)            evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 0)            koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.20/1.32	
2.20/1.32		start location:	koat_start
2.20/1.32	
2.20/1.32		leaf cost:	0
2.20/1.32	
2.20/1.32	
2.20/1.32	
2.20/1.32	Repeatedly propagating knowledge in problem 7 produces the following problem:
2.20/1.32	
2.20/1.32	8:	T:
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 1)            evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 1)            evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ar_1, Cost: 1)         evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
2.20/1.32	
2.20/1.32			(Comp: 2, Cost: 1)            evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
2.20/1.32	
2.20/1.32			(Comp: ar_1, Cost: 1)         evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4))
2.20/1.32	
2.20/1.32			(Comp: ar_1*ar_4, Cost: 1)    evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
2.20/1.32	
2.20/1.32			(Comp: ar_1, Cost: 1)         evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
2.20/1.32	
2.20/1.32			(Comp: ar_1*ar_4, Cost: 1)    evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 2, Cost: 1)            evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.20/1.32	
2.20/1.32			(Comp: 1, Cost: 0)            koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.20/1.32	
2.20/1.32		start location:	koat_start
2.20/1.32	
2.20/1.32		leaf cost:	0
2.20/1.32	
2.20/1.32	
2.20/1.32	
2.20/1.32	Complexity upper bound 3*ar_1 + 2*ar_1*ar_4 + 6
2.20/1.32	
2.20/1.32	
2.20/1.32	
2.20/1.32	Time: 0.121 sec (SMT: 0.100 sec)
2.20/1.32	
2.20/1.32	
2.20/1.32	----------------------------------------
2.20/1.32	
2.20/1.32	(2)
2.20/1.32	BOUNDS(1, n^2)
2.20/1.34	EOF