2.15/1.55	WORST_CASE(?, O(n^2))
2.15/1.56	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.15/1.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.15/1.56	
2.15/1.56	
2.15/1.56	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.15/1.56	
2.15/1.56	(0) CpxIntTrs
2.15/1.56	(1) Koat Proof [FINISHED, 280 ms]
2.15/1.56	(2) BOUNDS(1, n^2)
2.15/1.56	
2.15/1.56	
2.15/1.56	----------------------------------------
2.15/1.56	
2.15/1.56	(0)
2.15/1.56	Obligation:
2.15/1.56	Complexity Int TRS consisting of the following rules:
2.15/1.56	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
2.15/1.56	eval_speedSimpleMultipleDep_bb0_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(v_m, v_n, 0, 0)) :|: TRUE
2.15/1.56	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
2.15/1.56	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
2.15/1.56	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
2.15/1.56	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
2.15/1.56	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
2.15/1.56	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
2.15/1.56	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
2.15/1.56	
2.15/1.56	The start-symbols are:[eval_speedSimpleMultipleDep_start_4]
2.15/1.56	
2.15/1.56	
2.15/1.56	----------------------------------------
2.15/1.56	
2.15/1.56	(1) Koat Proof (FINISHED)
2.15/1.56	YES(?, 2*ar_2 + 2*ar_2*ar_3 + 2*ar_3 + 7)
2.15/1.56	
2.15/1.56	
2.15/1.56	
2.15/1.56	Initial complexity problem:
2.15/1.56	
2.15/1.56	1:	T:
2.15/1.56	
2.15/1.56			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56		start location:	koat_start
2.15/1.56	
2.15/1.56		leaf cost:	0
2.15/1.56	
2.15/1.56	
2.15/1.56	
2.15/1.56	Testing for reachability in the complexity graph removes the following transitions from problem 1:
2.15/1.56	
2.15/1.56		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 ]
2.15/1.56	
2.15/1.56		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 ]
2.15/1.56	
2.15/1.56	We thus obtain the following problem:
2.15/1.56	
2.15/1.56	2:	T:
2.15/1.56	
2.15/1.56			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56		start location:	koat_start
2.15/1.56	
2.15/1.56		leaf cost:	0
2.15/1.56	
2.15/1.56	
2.15/1.56	
2.15/1.56	Repeatedly propagating knowledge in problem 2 produces the following problem:
2.15/1.56	
2.15/1.56	3:	T:
2.15/1.56	
2.15/1.56			(Comp: ?, Cost: 1)    evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56		start location:	koat_start
2.15/1.56	
2.15/1.56		leaf cost:	0
2.15/1.56	
2.15/1.56	
2.15/1.56	
2.15/1.56	A polynomial rank function with
2.15/1.56	
2.15/1.56		Pol(evalspeedSimpleMultipleDepbb3in) = 1
2.15/1.56	
2.15/1.56		Pol(evalspeedSimpleMultipleDepstop) = 0
2.15/1.56	
2.15/1.56		Pol(evalspeedSimpleMultipleDepbb2in) = 2
2.15/1.56	
2.15/1.56		Pol(evalspeedSimpleMultipleDepbb1in) = 2
2.15/1.56	
2.15/1.56		Pol(evalspeedSimpleMultipleDepbb0in) = 2
2.15/1.56	
2.15/1.56		Pol(evalspeedSimpleMultipleDepstart) = 2
2.15/1.56	
2.15/1.56		Pol(koat_start) = 2
2.15/1.56	
2.15/1.56	orients all transitions weakly and the transitions
2.15/1.56	
2.15/1.56		evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3))
2.15/1.56	
2.15/1.56		evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.15/1.56	
2.15/1.56	strictly and produces the following problem:
2.15/1.56	
2.15/1.56	4:	T:
2.15/1.56	
2.15/1.56			(Comp: 2, Cost: 1)    evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56		start location:	koat_start
2.15/1.56	
2.15/1.56		leaf cost:	0
2.15/1.56	
2.15/1.56	
2.15/1.56	
2.15/1.56	Applied AI with 'oct' on problem 4 to obtain the following invariants:
2.15/1.56	
2.15/1.56	  For symbol evalspeedSimpleMultipleDepbb1in: X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
2.15/1.56	
2.15/1.56	  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
2.15/1.56	
2.15/1.56	  For symbol evalspeedSimpleMultipleDepbb3in: X_1 - X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
2.15/1.56	
2.15/1.56	
2.15/1.56	
2.15/1.56	
2.15/1.56	
2.15/1.56	This yielded the following problem:
2.15/1.56	
2.15/1.56	5:	T:
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(Comp: 1, Cost: 1)    evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56		start location:	koat_start
2.15/1.56	
2.15/1.56		leaf cost:	0
2.15/1.56	
2.15/1.56	
2.15/1.56	
2.15/1.56	A polynomial rank function with
2.15/1.56	
2.15/1.56		Pol(koat_start) = V_3
2.15/1.56	
2.15/1.56		Pol(evalspeedSimpleMultipleDepstart) = V_3
2.15/1.56	
2.15/1.56		Pol(evalspeedSimpleMultipleDepbb0in) = V_3
2.15/1.56	
2.15/1.56		Pol(evalspeedSimpleMultipleDepbb1in) = -V_1 + V_3
2.15/1.56	
2.15/1.56		Pol(evalspeedSimpleMultipleDepbb2in) = -V_1 + V_3
2.15/1.56	
2.15/1.56		Pol(evalspeedSimpleMultipleDepbb3in) = -V_1 + V_3
2.15/1.56	
2.15/1.56		Pol(evalspeedSimpleMultipleDepstop) = -V_1 + V_3
2.15/1.56	
2.15/1.56	orients all transitions weakly and the transition
2.15/1.56	
2.15/1.56		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 ]
2.15/1.56	
2.15/1.56	strictly and produces the following problem:
2.15/1.56	
2.15/1.56	6:	T:
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(Comp: 1, Cost: 1)       evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(Comp: 1, Cost: 1)       evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56		start location:	koat_start
2.15/1.56	
2.15/1.56		leaf cost:	0
2.15/1.56	
2.15/1.56	
2.15/1.56	
2.15/1.56	A polynomial rank function with
2.15/1.56	
2.15/1.56		Pol(evalspeedSimpleMultipleDepbb2in) = -V_2 + V_4
2.15/1.56	
2.15/1.56		Pol(evalspeedSimpleMultipleDepbb1in) = -V_2 + V_4
2.15/1.56	
2.15/1.56	and size complexities
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		S("evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))", 0-0) = 0
2.15/1.56	
2.15/1.56		S("evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))", 0-1) = 0
2.15/1.56	
2.15/1.56		S("evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))", 0-2) = ar_2
2.15/1.56	
2.15/1.56		S("evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))", 0-3) = ar_3
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56		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
2.15/1.56	
2.15/1.56	orients the transitions
2.15/1.56	
2.15/1.56		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 ]
2.15/1.56	
2.15/1.56		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 ]
2.15/1.56	
2.15/1.56	weakly and the transition
2.15/1.56	
2.15/1.56		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 ]
2.15/1.56	
2.15/1.56	strictly and produces the following problem:
2.15/1.56	
2.15/1.56	7:	T:
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(Comp: 1, Cost: 1)                   evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(Comp: 1, Cost: 1)                   evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56		start location:	koat_start
2.15/1.56	
2.15/1.56		leaf cost:	0
2.15/1.56	
2.15/1.56	
2.15/1.56	
2.15/1.56	Repeatedly propagating knowledge in problem 7 produces the following problem:
2.15/1.56	
2.15/1.56	8:	T:
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(Comp: 1, Cost: 1)                              evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(Comp: 1, Cost: 1)                              evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3))
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56			(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 ]
2.15/1.56	
2.15/1.56		start location:	koat_start
2.15/1.56	
2.15/1.56		leaf cost:	0
2.15/1.56	
2.15/1.56	
2.15/1.56	
2.15/1.56	Complexity upper bound 2*ar_2 + 2*ar_2*ar_3 + 2*ar_3 + 7
2.15/1.56	
2.15/1.56	
2.15/1.56	
2.15/1.56	Time: 0.229 sec (SMT: 0.192 sec)
2.15/1.56	
2.15/1.56	
2.15/1.56	----------------------------------------
2.15/1.56	
2.15/1.56	(2)
2.15/1.56	BOUNDS(1, n^2)
2.15/1.58	EOF