5.83/2.63	WORST_CASE(Omega(n^2), O(n^2))
6.06/2.64	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.06/2.64	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.06/2.64	
6.06/2.64	
6.06/2.64	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).
6.06/2.64	
6.06/2.64	(0) CpxIntTrs
6.06/2.64	(1) Koat Proof [FINISHED, 308 ms]
6.06/2.64	(2) BOUNDS(1, n^2)
6.06/2.64	(3) Loat Proof [FINISHED, 885 ms]
6.06/2.64	(4) BOUNDS(n^2, INF)
6.06/2.64	
6.06/2.64	
6.06/2.64	----------------------------------------
6.06/2.64	
6.06/2.64	(0)
6.06/2.64	Obligation:
6.06/2.64	Complexity Int TRS consisting of the following rules:
6.06/2.64	eval_speedpldi3_start(v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_speedpldi3_bb0_in(v_i_0, v_j_0, v_m, v_n)) :|: TRUE
6.06/2.64	eval_speedpldi3_bb0_in(v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_speedpldi3_0(v_i_0, v_j_0, v_m, v_n)) :|: TRUE
6.06/2.64	eval_speedpldi3_0(v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_speedpldi3_1(v_i_0, v_j_0, v_m, v_n)) :|: TRUE
6.06/2.64	eval_speedpldi3_1(v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_speedpldi3_2(v_i_0, v_j_0, v_m, v_n)) :|: TRUE
6.06/2.64	eval_speedpldi3_2(v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_speedpldi3_bb3_in(v_i_0, v_j_0, v_m, v_n)) :|: v_m <= 0
6.06/2.64	eval_speedpldi3_2(v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_speedpldi3_bb3_in(v_i_0, v_j_0, v_m, v_n)) :|: v_n <= v_m
6.06/2.64	eval_speedpldi3_2(v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_speedpldi3_bb1_in(0, 0, v_m, v_n)) :|: v_m > 0 && v_n > v_m
6.06/2.64	eval_speedpldi3_bb1_in(v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_speedpldi3_bb2_in(v_i_0, v_j_0, v_m, v_n)) :|: v_i_0 < v_n
6.06/2.64	eval_speedpldi3_bb1_in(v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_speedpldi3_bb3_in(v_i_0, v_j_0, v_m, v_n)) :|: v_i_0 >= v_n
6.06/2.64	eval_speedpldi3_bb2_in(v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_speedpldi3_bb1_in(v_i_0, v_j_0 + 1, v_m, v_n)) :|: v_j_0 < v_m
6.06/2.64	eval_speedpldi3_bb2_in(v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_speedpldi3_bb1_in(v_i_0 + 1, v_j_0 + 1, v_m, v_n)) :|: v_j_0 < v_m && v_j_0 >= v_m
6.06/2.64	eval_speedpldi3_bb2_in(v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_speedpldi3_bb1_in(v_i_0, 0, v_m, v_n)) :|: v_j_0 >= v_m && v_j_0 < v_m
6.06/2.64	eval_speedpldi3_bb2_in(v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_speedpldi3_bb1_in(v_i_0 + 1, 0, v_m, v_n)) :|: v_j_0 >= v_m
6.06/2.64	eval_speedpldi3_bb3_in(v_i_0, v_j_0, v_m, v_n) -> Com_1(eval_speedpldi3_stop(v_i_0, v_j_0, v_m, v_n)) :|: TRUE
6.06/2.64	
6.06/2.64	The start-symbols are:[eval_speedpldi3_start_4]
6.06/2.64	
6.06/2.64	
6.06/2.64	----------------------------------------
6.06/2.64	
6.06/2.64	(1) Koat Proof (FINISHED)
6.06/2.64	YES(?, 2*ar_1 + 2*ar_0*ar_1 + 2*ar_0 + 12)
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Initial complexity problem:
6.06/2.64	
6.06/2.64	1:	T:
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi30(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi30(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi31(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi31(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi32(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_0 >= ar_3 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, ar_3 + 1)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_0 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= ar_0 /\ ar_0 >= ar_3 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= ar_0 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.06/2.64	
6.06/2.64		start location:	koat_start
6.06/2.64	
6.06/2.64		leaf cost:	0
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Testing for reachability in the complexity graph removes the following transitions from problem 1:
6.06/2.64	
6.06/2.64		evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, ar_3 + 1)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_0 ]
6.06/2.64	
6.06/2.64		evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= ar_0 /\ ar_0 >= ar_3 + 1 ]
6.06/2.64	
6.06/2.64	We thus obtain the following problem:
6.06/2.64	
6.06/2.64	2:	T:
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= ar_0 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_0 >= ar_3 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi31(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi32(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi30(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi31(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi30(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.06/2.64	
6.06/2.64		start location:	koat_start
6.06/2.64	
6.06/2.64		leaf cost:	0
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Repeatedly propagating knowledge in problem 2 produces the following problem:
6.06/2.64	
6.06/2.64	3:	T:
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= ar_0 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_0 >= ar_3 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi31(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi32(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi30(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi31(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi30(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.06/2.64	
6.06/2.64		start location:	koat_start
6.06/2.64	
6.06/2.64		leaf cost:	0
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	A polynomial rank function with
6.06/2.64	
6.06/2.64		Pol(evalspeedpldi3bb1in) = 2
6.06/2.64	
6.06/2.64		Pol(evalspeedpldi3bb3in) = 1
6.06/2.64	
6.06/2.64		Pol(evalspeedpldi3bb2in) = 2
6.06/2.64	
6.06/2.64		Pol(evalspeedpldi3stop) = 0
6.06/2.64	
6.06/2.64		Pol(evalspeedpldi32) = 2
6.06/2.64	
6.06/2.64		Pol(evalspeedpldi31) = 2
6.06/2.64	
6.06/2.64		Pol(evalspeedpldi30) = 2
6.06/2.64	
6.06/2.64		Pol(evalspeedpldi3bb0in) = 2
6.06/2.64	
6.06/2.64		Pol(evalspeedpldi3start) = 2
6.06/2.64	
6.06/2.64		Pol(koat_start) = 2
6.06/2.64	
6.06/2.64	orients all transitions weakly and the transitions
6.06/2.64	
6.06/2.64		evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64		evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ]
6.06/2.64	
6.06/2.64	strictly and produces the following problem:
6.06/2.64	
6.06/2.64	4:	T:
6.06/2.64	
6.06/2.64			(Comp: 2, Cost: 1)    evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= ar_0 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_0 >= ar_3 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: 2, Cost: 1)    evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi31(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi32(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi30(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi31(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi30(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.06/2.64	
6.06/2.64		start location:	koat_start
6.06/2.64	
6.06/2.64		leaf cost:	0
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Applied AI with 'oct' on problem 4 to obtain the following invariants:
6.06/2.64	
6.06/2.64	  For symbol evalspeedpldi3bb1in: X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
6.06/2.64	
6.06/2.64	  For symbol evalspeedpldi3bb2in: X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	This yielded the following problem:
6.06/2.64	
6.06/2.64	5:	T:
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi30(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi30(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi31(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi31(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi32(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)    evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: 2, Cost: 1)    evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)    evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
6.06/2.64	
6.06/2.64			(Comp: 2, Cost: 1)    evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ]
6.06/2.64	
6.06/2.64		start location:	koat_start
6.06/2.64	
6.06/2.64		leaf cost:	0
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	A polynomial rank function with
6.06/2.64	
6.06/2.64		Pol(evalspeedpldi3bb2in) = V_2 - V_3
6.06/2.64	
6.06/2.64		Pol(evalspeedpldi3bb1in) = V_2 - V_3
6.06/2.64	
6.06/2.64	and size complexities
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 ]", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 ]", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 ]", 0-2) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 ]", 0-3) = 0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-2) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-3) = 0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-2) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-3) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-2) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-3) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_1 + ar_2
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-2) = 0
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-3) = 0
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-2) = ar_2
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-3) = ar_3
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3
6.06/2.64	
6.06/2.64		S("evalspeedpldi31(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi32(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi31(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi32(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi31(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi32(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
6.06/2.64	
6.06/2.64		S("evalspeedpldi31(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi32(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
6.06/2.64	
6.06/2.64		S("evalspeedpldi30(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi31(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi30(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi31(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi30(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi31(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
6.06/2.64	
6.06/2.64		S("evalspeedpldi30(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi31(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi30(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi30(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi30(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi30(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
6.06/2.64	
6.06/2.64		S("evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
6.06/2.64	
6.06/2.64		S("evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
6.06/2.64	
6.06/2.64		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
6.06/2.64	
6.06/2.64		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
6.06/2.64	
6.06/2.64	orients the transitions
6.06/2.64	
6.06/2.64		evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
6.06/2.64	
6.06/2.64		evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
6.06/2.64	
6.06/2.64		evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 + 1 ]
6.06/2.64	
6.06/2.64	weakly and the transition
6.06/2.64	
6.06/2.64		evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
6.06/2.64	
6.06/2.64	strictly and produces the following problem:
6.06/2.64	
6.06/2.64	6:	T:
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)       evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)       evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi30(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)       evalspeedpldi30(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi31(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)       evalspeedpldi31(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi32(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)       evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)       evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)       evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: 2, Cost: 1)       evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)       evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)       evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ar_1, Cost: 1)    evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
6.06/2.64	
6.06/2.64			(Comp: 2, Cost: 1)       evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ]
6.06/2.64	
6.06/2.64		start location:	koat_start
6.06/2.64	
6.06/2.64		leaf cost:	0
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	A polynomial rank function with
6.06/2.64	
6.06/2.64		Pol(evalspeedpldi3bb2in) = V_1 - V_4
6.06/2.64	
6.06/2.64		Pol(evalspeedpldi3bb1in) = V_1 - V_4
6.06/2.64	
6.06/2.64	and size complexities
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 ]", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 ]", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 ]", 0-2) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 ]", 0-3) = 0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-2) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-3) = 0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-2) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-3) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-2) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-3) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_1 + ar_2
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-2) = 0
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-3) = 0
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-2) = ar_2
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-3) = ar_3
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2
6.06/2.64	
6.06/2.64		S("evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3
6.06/2.64	
6.06/2.64		S("evalspeedpldi31(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi32(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi31(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi32(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi31(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi32(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
6.06/2.64	
6.06/2.64		S("evalspeedpldi31(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi32(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
6.06/2.64	
6.06/2.64		S("evalspeedpldi30(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi31(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi30(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi31(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi30(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi31(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
6.06/2.64	
6.06/2.64		S("evalspeedpldi30(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi31(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi30(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi30(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi30(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
6.06/2.64	
6.06/2.64		S("evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi30(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
6.06/2.64	
6.06/2.64		S("evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
6.06/2.64	
6.06/2.64		S("evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
6.06/2.64	
6.06/2.64		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
6.06/2.64	
6.06/2.64		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
6.06/2.64	
6.06/2.64		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
6.06/2.64	
6.06/2.64		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
6.06/2.64	
6.06/2.64	orients the transitions
6.06/2.64	
6.06/2.64		evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
6.06/2.64	
6.06/2.64		evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 + 1 ]
6.06/2.64	
6.06/2.64	weakly and the transition
6.06/2.64	
6.06/2.64		evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
6.06/2.64	
6.06/2.64	strictly and produces the following problem:
6.06/2.64	
6.06/2.64	7:	T:
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 0)                   koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)                   evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)                   evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi30(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)                   evalspeedpldi30(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi31(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)                   evalspeedpldi31(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi32(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)                   evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)                   evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)                   evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: 2, Cost: 1)                   evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: ?, Cost: 1)                   evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ar_0*ar_1 + ar_0, Cost: 1)    evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ar_1, Cost: 1)                evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
6.06/2.64	
6.06/2.64			(Comp: 2, Cost: 1)                   evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ]
6.06/2.64	
6.06/2.64		start location:	koat_start
6.06/2.64	
6.06/2.64		leaf cost:	0
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Repeatedly propagating knowledge in problem 7 produces the following problem:
6.06/2.64	
6.06/2.64	8:	T:
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 0)                              koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)                              evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)                              evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi30(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)                              evalspeedpldi30(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi31(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)                              evalspeedpldi31(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi32(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)                              evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)                              evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.06/2.64	
6.06/2.64			(Comp: 1, Cost: 1)                              evalspeedpldi32(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: 2, Cost: 1)                              evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3))
6.06/2.64	
6.06/2.64			(Comp: ar_1 + ar_0*ar_1 + ar_0 + 1, Cost: 1)    evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ar_0*ar_1 + ar_0, Cost: 1)               evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
6.06/2.64	
6.06/2.64			(Comp: ar_1, Cost: 1)                           evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
6.06/2.64	
6.06/2.64			(Comp: 2, Cost: 1)                              evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ]
6.06/2.64	
6.06/2.64		start location:	koat_start
6.06/2.64	
6.06/2.64		leaf cost:	0
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Complexity upper bound 2*ar_1 + 2*ar_0*ar_1 + 2*ar_0 + 12
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Time: 0.348 sec (SMT: 0.268 sec)
6.06/2.64	
6.06/2.64	
6.06/2.64	----------------------------------------
6.06/2.64	
6.06/2.64	(2)
6.06/2.64	BOUNDS(1, n^2)
6.06/2.64	
6.06/2.64	----------------------------------------
6.06/2.64	
6.06/2.64	(3) Loat Proof (FINISHED)
6.06/2.64	
6.06/2.64	
6.06/2.64	### Pre-processing the ITS problem ###
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Initial linear ITS problem
6.06/2.64	
6.06/2.64	   Start location: evalspeedpldi3start
6.06/2.64	
6.06/2.64	      0: evalspeedpldi3start -> evalspeedpldi3bb0in : [], cost: 1
6.06/2.64	
6.06/2.64	      1: evalspeedpldi3bb0in -> evalspeedpldi30 : [], cost: 1
6.06/2.64	
6.06/2.64	      2: evalspeedpldi30 -> evalspeedpldi31 : [], cost: 1
6.06/2.64	
6.06/2.64	      3: evalspeedpldi31 -> evalspeedpldi32 : [], cost: 1
6.06/2.64	
6.06/2.64	      4: evalspeedpldi32 -> evalspeedpldi3bb3in : [ 0>=A ], cost: 1
6.06/2.64	
6.06/2.64	      5: evalspeedpldi32 -> evalspeedpldi3bb3in : [ A>=B ], cost: 1
6.06/2.64	
6.06/2.64	      6: evalspeedpldi32 -> evalspeedpldi3bb1in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 1
6.06/2.64	
6.06/2.64	      7: evalspeedpldi3bb1in -> evalspeedpldi3bb2in : [ B>=1+C ], cost: 1
6.06/2.64	
6.06/2.64	      8: evalspeedpldi3bb1in -> evalspeedpldi3bb3in : [ C>=B ], cost: 1
6.06/2.64	
6.06/2.64	      9: evalspeedpldi3bb2in -> evalspeedpldi3bb1in : D'=1+D, [ A>=1+D ], cost: 1
6.06/2.64	
6.06/2.64	     10: evalspeedpldi3bb2in -> evalspeedpldi3bb1in : C'=1+C, D'=1+D, [ A>=1+D && D>=A ], cost: 1
6.06/2.64	
6.06/2.64	     11: evalspeedpldi3bb2in -> evalspeedpldi3bb1in : D'=0, [ D>=A && A>=1+D ], cost: 1
6.06/2.64	
6.06/2.64	     12: evalspeedpldi3bb2in -> evalspeedpldi3bb1in : C'=1+C, D'=0, [ D>=A ], cost: 1
6.06/2.64	
6.06/2.64	     13: evalspeedpldi3bb3in -> evalspeedpldi3stop : [], cost: 1
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Removed unreachable and leaf rules:
6.06/2.64	
6.06/2.64	   Start location: evalspeedpldi3start
6.06/2.64	
6.06/2.64	      0: evalspeedpldi3start -> evalspeedpldi3bb0in : [], cost: 1
6.06/2.64	
6.06/2.64	      1: evalspeedpldi3bb0in -> evalspeedpldi30 : [], cost: 1
6.06/2.64	
6.06/2.64	      2: evalspeedpldi30 -> evalspeedpldi31 : [], cost: 1
6.06/2.64	
6.06/2.64	      3: evalspeedpldi31 -> evalspeedpldi32 : [], cost: 1
6.06/2.64	
6.06/2.64	      6: evalspeedpldi32 -> evalspeedpldi3bb1in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 1
6.06/2.64	
6.06/2.64	      7: evalspeedpldi3bb1in -> evalspeedpldi3bb2in : [ B>=1+C ], cost: 1
6.06/2.64	
6.06/2.64	      9: evalspeedpldi3bb2in -> evalspeedpldi3bb1in : D'=1+D, [ A>=1+D ], cost: 1
6.06/2.64	
6.06/2.64	     10: evalspeedpldi3bb2in -> evalspeedpldi3bb1in : C'=1+C, D'=1+D, [ A>=1+D && D>=A ], cost: 1
6.06/2.64	
6.06/2.64	     11: evalspeedpldi3bb2in -> evalspeedpldi3bb1in : D'=0, [ D>=A && A>=1+D ], cost: 1
6.06/2.64	
6.06/2.64	     12: evalspeedpldi3bb2in -> evalspeedpldi3bb1in : C'=1+C, D'=0, [ D>=A ], cost: 1
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Removed rules with unsatisfiable guard:
6.06/2.64	
6.06/2.64	   Start location: evalspeedpldi3start
6.06/2.64	
6.06/2.64	      0: evalspeedpldi3start -> evalspeedpldi3bb0in : [], cost: 1
6.06/2.64	
6.06/2.64	      1: evalspeedpldi3bb0in -> evalspeedpldi30 : [], cost: 1
6.06/2.64	
6.06/2.64	      2: evalspeedpldi30 -> evalspeedpldi31 : [], cost: 1
6.06/2.64	
6.06/2.64	      3: evalspeedpldi31 -> evalspeedpldi32 : [], cost: 1
6.06/2.64	
6.06/2.64	      6: evalspeedpldi32 -> evalspeedpldi3bb1in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 1
6.06/2.64	
6.06/2.64	      7: evalspeedpldi3bb1in -> evalspeedpldi3bb2in : [ B>=1+C ], cost: 1
6.06/2.64	
6.06/2.64	      9: evalspeedpldi3bb2in -> evalspeedpldi3bb1in : D'=1+D, [ A>=1+D ], cost: 1
6.06/2.64	
6.06/2.64	     12: evalspeedpldi3bb2in -> evalspeedpldi3bb1in : C'=1+C, D'=0, [ D>=A ], cost: 1
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	### Simplification by acceleration and chaining ###
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Eliminated locations (on linear paths):
6.06/2.64	
6.06/2.64	   Start location: evalspeedpldi3start
6.06/2.64	
6.06/2.64	     17: evalspeedpldi3start -> evalspeedpldi3bb1in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 5
6.06/2.64	
6.06/2.64	      7: evalspeedpldi3bb1in -> evalspeedpldi3bb2in : [ B>=1+C ], cost: 1
6.06/2.64	
6.06/2.64	      9: evalspeedpldi3bb2in -> evalspeedpldi3bb1in : D'=1+D, [ A>=1+D ], cost: 1
6.06/2.64	
6.06/2.64	     12: evalspeedpldi3bb2in -> evalspeedpldi3bb1in : C'=1+C, D'=0, [ D>=A ], cost: 1
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Eliminated locations (on tree-shaped paths):
6.06/2.64	
6.06/2.64	   Start location: evalspeedpldi3start
6.06/2.64	
6.06/2.64	     17: evalspeedpldi3start -> evalspeedpldi3bb1in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 5
6.06/2.64	
6.06/2.64	     18: evalspeedpldi3bb1in -> evalspeedpldi3bb1in : D'=1+D, [ B>=1+C && A>=1+D ], cost: 2
6.06/2.64	
6.06/2.64	     19: evalspeedpldi3bb1in -> evalspeedpldi3bb1in : C'=1+C, D'=0, [ B>=1+C && D>=A ], cost: 2
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Accelerating simple loops of location 5.
6.06/2.64	
6.06/2.64	   Accelerating the following rules:
6.06/2.64	
6.06/2.64	     18: evalspeedpldi3bb1in -> evalspeedpldi3bb1in : D'=1+D, [ B>=1+C && A>=1+D ], cost: 2
6.06/2.64	
6.06/2.64	     19: evalspeedpldi3bb1in -> evalspeedpldi3bb1in : C'=1+C, D'=0, [ B>=1+C && D>=A ], cost: 2
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	   Accelerated rule 18 with metering function -D+A, yielding the new rule 20.
6.06/2.64	
6.06/2.64	   Accelerated rule 19 with metering function -C+B (after strengthening guard), yielding the new rule 21.
6.06/2.64	
6.06/2.64	   Nested simple loops 19 (outer loop) and 20 (inner loop) with metering function -1-C+B, resulting in the new rules: 22, 23.
6.06/2.64	
6.06/2.64	   Removing the simple loops: 18 19.
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Accelerated all simple loops using metering functions (where possible):
6.06/2.64	
6.06/2.64	   Start location: evalspeedpldi3start
6.06/2.64	
6.06/2.64	     17: evalspeedpldi3start -> evalspeedpldi3bb1in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 5
6.06/2.64	
6.06/2.64	     20: evalspeedpldi3bb1in -> evalspeedpldi3bb1in : D'=A, [ B>=1+C && A>=1+D ], cost: -2*D+2*A
6.06/2.64	
6.06/2.64	     21: evalspeedpldi3bb1in -> evalspeedpldi3bb1in : C'=B, D'=0, [ B>=1+C && D>=A && 0>=A ], cost: -2*C+2*B
6.06/2.64	
6.06/2.64	     22: evalspeedpldi3bb1in -> evalspeedpldi3bb1in : C'=-1+B, D'=A, [ D>=A && B>=2+C && A>=1 ], cost: -2-2*C-2*(1+C-B)*A+2*B
6.06/2.64	
6.06/2.64	     23: evalspeedpldi3bb1in -> evalspeedpldi3bb1in : C'=-1+B, D'=A, [ A>=1+D && B>=2+C && A>=1 ], cost: -2-2*C-2*(1+C-B)*A-2*D+2*A+2*B
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Chained accelerated rules (with incoming rules):
6.06/2.64	
6.06/2.64	   Start location: evalspeedpldi3start
6.06/2.64	
6.06/2.64	     17: evalspeedpldi3start -> evalspeedpldi3bb1in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 5
6.06/2.64	
6.06/2.64	     24: evalspeedpldi3start -> evalspeedpldi3bb1in : C'=0, D'=A, [ A>=1 && B>=1+A && B>=1 ], cost: 5+2*A
6.06/2.64	
6.06/2.64	     25: evalspeedpldi3start -> evalspeedpldi3bb1in : C'=-1+B, D'=A, [ A>=1 && B>=1+A && B>=2 ], cost: 3+2*A+2*(-1+B)*A+2*B
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Removed unreachable locations (and leaf rules with constant cost):
6.06/2.64	
6.06/2.64	   Start location: evalspeedpldi3start
6.06/2.64	
6.06/2.64	     24: evalspeedpldi3start -> evalspeedpldi3bb1in : C'=0, D'=A, [ A>=1 && B>=1+A && B>=1 ], cost: 5+2*A
6.06/2.64	
6.06/2.64	     25: evalspeedpldi3start -> evalspeedpldi3bb1in : C'=-1+B, D'=A, [ A>=1 && B>=1+A && B>=2 ], cost: 3+2*A+2*(-1+B)*A+2*B
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	### Computing asymptotic complexity ###
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Fully simplified ITS problem
6.06/2.64	
6.06/2.64	   Start location: evalspeedpldi3start
6.06/2.64	
6.06/2.64	     24: evalspeedpldi3start -> evalspeedpldi3bb1in : C'=0, D'=A, [ A>=1 && B>=1+A && B>=1 ], cost: 5+2*A
6.06/2.64	
6.06/2.64	     25: evalspeedpldi3start -> evalspeedpldi3bb1in : C'=-1+B, D'=A, [ A>=1 && B>=1+A && B>=2 ], cost: 3+2*A+2*(-1+B)*A+2*B
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Computing asymptotic complexity for rule 24
6.06/2.64	
6.06/2.64	   Solved the limit problem by the following transformations:
6.06/2.64	
6.06/2.64	      Created initial limit problem:
6.06/2.64	
6.06/2.64	      5+2*A (+), A (+/+!), -A+B (+/+!) [not solved]
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	      removing all constraints (solved by SMT)
6.06/2.64	
6.06/2.64	      resulting limit problem: [solved]
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	      applying transformation rule (C) using substitution {A==n,B==2*n}
6.06/2.64	
6.06/2.64	      resulting limit problem:
6.06/2.64	
6.06/2.64	      [solved]
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	   Solution:
6.06/2.64	
6.06/2.64	      A / n
6.06/2.64	
6.06/2.64	      B / 2*n
6.06/2.64	
6.06/2.64	   Resulting cost 5+2*n has complexity: Poly(n^1)
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Found new complexity Poly(n^1).
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Computing asymptotic complexity for rule 25
6.06/2.64	
6.06/2.64	   Solved the limit problem by the following transformations:
6.06/2.64	
6.06/2.64	      Created initial limit problem:
6.06/2.64	
6.06/2.64	      3+2*A*B+2*B (+), A (+/+!), -A+B (+/+!) [not solved]
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	      applying transformation rule (C) using substitution {A==1}
6.06/2.64	
6.06/2.64	      resulting limit problem:
6.06/2.64	
6.06/2.64	      1 (+/+!), -1+B (+/+!), 3+4*B (+) [not solved]
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	      applying transformation rule (C) using substitution {B==1+A}
6.06/2.64	
6.06/2.64	      resulting limit problem:
6.06/2.64	
6.06/2.64	      1 (+/+!), A (+/+!), 7+4*A (+) [not solved]
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	      applying transformation rule (B), deleting 1 (+/+!)
6.06/2.64	
6.06/2.64	      resulting limit problem:
6.06/2.64	
6.06/2.64	      A (+/+!), 7+4*A (+) [not solved]
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	      removing all constraints (solved by SMT)
6.06/2.64	
6.06/2.64	      resulting limit problem: [solved]
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	      applying transformation rule (C) using substitution {A==n}
6.06/2.64	
6.06/2.64	      resulting limit problem:
6.06/2.64	
6.06/2.64	      [solved]
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	   Solved the limit problem by the following transformations:
6.06/2.64	
6.06/2.64	      Created initial limit problem:
6.06/2.64	
6.06/2.64	      3+2*A*B+2*B (+), A (+/+!), -A+B (+/+!) [not solved]
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	      removing all constraints (solved by SMT)
6.06/2.64	
6.06/2.64	      resulting limit problem: [solved]
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	      applying transformation rule (C) using substitution {A==1+n,B==2+n}
6.06/2.64	
6.06/2.64	      resulting limit problem:
6.06/2.64	
6.06/2.64	      [solved]
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	   Solution:
6.06/2.64	
6.06/2.64	      A / 1+n
6.06/2.64	
6.06/2.64	      B / 2+n
6.06/2.64	
6.06/2.64	   Resulting cost 11+2*n^2+8*n has complexity: Poly(n^2)
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Found new complexity Poly(n^2).
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	Obtained the following overall complexity (w.r.t. the length of the input n):
6.06/2.64	
6.06/2.64	   Complexity:  Poly(n^2)
6.06/2.64	
6.06/2.64	   Cpx degree:  2
6.06/2.64	
6.06/2.64	   Solved cost: 11+2*n^2+8*n
6.06/2.64	
6.06/2.64	   Rule cost:   3+2*A+2*(-1+B)*A+2*B
6.06/2.64	
6.06/2.64	   Rule guard:  [ A>=1 && B>=1+A ]
6.06/2.64	
6.06/2.64	
6.06/2.64	
6.06/2.64	WORST_CASE(Omega(n^2),?)
6.06/2.64	
6.06/2.64	
6.06/2.64	----------------------------------------
6.06/2.64	
6.06/2.64	(4)
6.06/2.64	BOUNDS(n^2, INF)
6.06/2.67	EOF