2.27/1.37	WORST_CASE(?, O(n^1))
2.27/1.38	proof of /export/starexec/sandbox2/output/output_files/bench.koat
2.27/1.38	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.27/1.38	
2.27/1.38	
2.27/1.38	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.27/1.38	
2.27/1.38	(0) CpxIntTrs
2.27/1.38	(1) Koat Proof [FINISHED, 76 ms]
2.27/1.38	(2) BOUNDS(1, n^1)
2.27/1.38	
2.27/1.38	
2.27/1.38	----------------------------------------
2.27/1.38	
2.27/1.38	(0)
2.27/1.38	Obligation:
2.27/1.38	Complexity Int TRS consisting of the following rules:
2.27/1.38	eval_exmini_start(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_exmini_bb0_in(v_.0, v_.01, v_.02, v_i, v_j, v_k)) :|: TRUE
2.27/1.38	eval_exmini_bb0_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_exmini_bb1_in(v_i, v_j, v_k, v_i, v_j, v_k)) :|: TRUE
2.27/1.38	eval_exmini_bb1_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_exmini_bb2_in(v_.0, v_.01, v_.02, v_i, v_j, v_k)) :|: v_.0 <= 100 && v_.01 <= v_.02
2.27/1.38	eval_exmini_bb1_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_exmini_bb3_in(v_.0, v_.01, v_.02, v_i, v_j, v_k)) :|: v_.0 > 100
2.27/1.38	eval_exmini_bb1_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_exmini_bb3_in(v_.0, v_.01, v_.02, v_i, v_j, v_k)) :|: v_.01 > v_.02
2.27/1.39	eval_exmini_bb2_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_exmini_bb1_in(v_.01, v_.0 + 1, v_.02 - 1, v_i, v_j, v_k)) :|: TRUE
2.27/1.39	eval_exmini_bb3_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_exmini_stop(v_.0, v_.01, v_.02, v_i, v_j, v_k)) :|: TRUE
2.27/1.39	
2.27/1.39	The start-symbols are:[eval_exmini_start_6]
2.27/1.39	
2.27/1.39	
2.27/1.39	----------------------------------------
2.27/1.39	
2.27/1.39	(1) Koat Proof (FINISHED)
2.27/1.39	YES(?, 2*ar_1 + 2*ar_3 + 2*ar_5 + 210)
2.27/1.39	
2.27/1.39	
2.27/1.39	
2.27/1.39	Initial complexity problem:
2.27/1.39	
2.27/1.39	1:	T:
2.27/1.39	
2.27/1.39			(Comp: ?, Cost: 1)    evalexministart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.27/1.39	
2.27/1.39			(Comp: ?, Cost: 1)    evalexminibb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5))
2.27/1.39	
2.27/1.39			(Comp: ?, Cost: 1)    evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_0 /\ ar_4 >= ar_2 ]
2.27/1.39	
2.27/1.39			(Comp: ?, Cost: 1)    evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 101 ]
2.27/1.39	
2.27/1.39			(Comp: ?, Cost: 1)    evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ]
2.27/1.39	
2.27/1.39			(Comp: ?, Cost: 1)    evalexminibb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb1in(ar_2, ar_1, ar_0 + 1, ar_3, ar_4 - 1, ar_5))
2.27/1.39	
2.27/1.39			(Comp: ?, Cost: 1)    evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexministop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.27/1.39	
2.27/1.39			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexministart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.27/1.39	
2.27/1.39		start location:	koat_start
2.27/1.39	
2.27/1.39		leaf cost:	0
2.27/1.39	
2.27/1.39	
2.27/1.39	
2.27/1.39	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.27/1.39	
2.27/1.39	2:	T:
2.27/1.39	
2.27/1.39			(Comp: 1, Cost: 1)    evalexministart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.27/1.39	
2.27/1.39			(Comp: 1, Cost: 1)    evalexminibb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5))
2.27/1.39	
2.27/1.39			(Comp: ?, Cost: 1)    evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_0 /\ ar_4 >= ar_2 ]
2.27/1.39	
2.27/1.39			(Comp: ?, Cost: 1)    evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 101 ]
2.27/1.39	
2.27/1.39			(Comp: ?, Cost: 1)    evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ]
2.27/1.39	
2.27/1.39			(Comp: ?, Cost: 1)    evalexminibb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb1in(ar_2, ar_1, ar_0 + 1, ar_3, ar_4 - 1, ar_5))
2.27/1.39	
2.27/1.39			(Comp: ?, Cost: 1)    evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexministop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.27/1.39	
2.27/1.39			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexministart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.27/1.39	
2.27/1.39		start location:	koat_start
2.27/1.39	
2.27/1.39		leaf cost:	0
2.27/1.39	
2.27/1.39	
2.27/1.39	
2.27/1.39	A polynomial rank function with
2.27/1.39	
2.27/1.39		Pol(evalexministart) = 2
2.27/1.39	
2.27/1.39		Pol(evalexminibb0in) = 2
2.27/1.39	
2.27/1.39		Pol(evalexminibb1in) = 2
2.27/1.39	
2.27/1.39		Pol(evalexminibb2in) = 2
2.27/1.39	
2.27/1.39		Pol(evalexminibb3in) = 1
2.27/1.39	
2.27/1.39		Pol(evalexministop) = 0
2.27/1.39	
2.27/1.39		Pol(koat_start) = 2
2.27/1.39	
2.27/1.39	orients all transitions weakly and the transitions
2.27/1.39	
2.27/1.39		evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexministop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.27/1.39	
2.27/1.39		evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ]
2.27/1.39	
2.27/1.39		evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 101 ]
2.27/1.39	
2.27/1.39	strictly and produces the following problem:
2.27/1.39	
2.27/1.39	3:	T:
2.27/1.39	
2.27/1.39			(Comp: 1, Cost: 1)    evalexministart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.27/1.39	
2.27/1.39			(Comp: 1, Cost: 1)    evalexminibb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5))
2.27/1.39	
2.27/1.39			(Comp: ?, Cost: 1)    evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_0 /\ ar_4 >= ar_2 ]
2.27/1.39	
2.27/1.39			(Comp: 2, Cost: 1)    evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 101 ]
2.27/1.39	
2.27/1.39			(Comp: 2, Cost: 1)    evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ]
2.27/1.39	
2.27/1.39			(Comp: ?, Cost: 1)    evalexminibb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb1in(ar_2, ar_1, ar_0 + 1, ar_3, ar_4 - 1, ar_5))
2.27/1.39	
2.27/1.39			(Comp: 2, Cost: 1)    evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexministop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.27/1.39	
2.27/1.39			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexministart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.27/1.39	
2.27/1.39		start location:	koat_start
2.27/1.39	
2.27/1.39		leaf cost:	0
2.27/1.39	
2.27/1.39	
2.27/1.39	
2.27/1.39	A polynomial rank function with
2.27/1.39	
2.27/1.39		Pol(evalexministart) = -V_2 - V_4 + V_6 + 101
2.27/1.39	
2.27/1.39		Pol(evalexminibb0in) = -V_2 - V_4 + V_6 + 101
2.27/1.39	
2.27/1.39		Pol(evalexminibb1in) = -V_1 - V_3 + V_5 + 101
2.27/1.39	
2.27/1.39		Pol(evalexminibb2in) = -V_1 - V_3 + V_5 + 99
2.27/1.39	
2.27/1.39		Pol(evalexminibb3in) = -V_1 - V_3 + V_5
2.27/1.39	
2.27/1.39		Pol(evalexministop) = -V_1 - V_3 + V_5
2.27/1.39	
2.27/1.39		Pol(koat_start) = -V_2 - V_4 + V_6 + 101
2.27/1.39	
2.27/1.39	orients all transitions weakly and the transition
2.27/1.39	
2.27/1.39		evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_0 /\ ar_4 >= ar_2 ]
2.27/1.39	
2.27/1.39	strictly and produces the following problem:
2.27/1.39	
2.27/1.39	4:	T:
2.27/1.39	
2.27/1.39			(Comp: 1, Cost: 1)                           evalexministart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.27/1.39	
2.27/1.39			(Comp: 1, Cost: 1)                           evalexminibb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5))
2.27/1.39	
2.27/1.39			(Comp: ar_1 + ar_3 + ar_5 + 101, Cost: 1)    evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_0 /\ ar_4 >= ar_2 ]
2.27/1.39	
2.27/1.39			(Comp: 2, Cost: 1)                           evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 101 ]
2.27/1.39	
2.27/1.39			(Comp: 2, Cost: 1)                           evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ]
2.27/1.39	
2.27/1.39			(Comp: ?, Cost: 1)                           evalexminibb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb1in(ar_2, ar_1, ar_0 + 1, ar_3, ar_4 - 1, ar_5))
2.27/1.39	
2.27/1.39			(Comp: 2, Cost: 1)                           evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexministop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.27/1.39	
2.27/1.39			(Comp: 1, Cost: 0)                           koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexministart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.27/1.39	
2.27/1.39		start location:	koat_start
2.27/1.39	
2.27/1.39		leaf cost:	0
2.27/1.39	
2.27/1.39	
2.27/1.39	
2.27/1.39	Repeatedly propagating knowledge in problem 4 produces the following problem:
2.27/1.39	
2.27/1.39	5:	T:
2.27/1.39	
2.27/1.39			(Comp: 1, Cost: 1)                           evalexministart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.27/1.39	
2.27/1.39			(Comp: 1, Cost: 1)                           evalexminibb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5))
2.27/1.39	
2.27/1.39			(Comp: ar_1 + ar_3 + ar_5 + 101, Cost: 1)    evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_0 /\ ar_4 >= ar_2 ]
2.27/1.39	
2.27/1.39			(Comp: 2, Cost: 1)                           evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 101 ]
2.27/1.39	
2.27/1.39			(Comp: 2, Cost: 1)                           evalexminibb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ]
2.27/1.39	
2.27/1.39			(Comp: ar_1 + ar_3 + ar_5 + 101, Cost: 1)    evalexminibb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexminibb1in(ar_2, ar_1, ar_0 + 1, ar_3, ar_4 - 1, ar_5))
2.27/1.39	
2.27/1.39			(Comp: 2, Cost: 1)                           evalexminibb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexministop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.27/1.39	
2.27/1.39			(Comp: 1, Cost: 0)                           koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalexministart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.27/1.39	
2.27/1.39		start location:	koat_start
2.27/1.39	
2.27/1.39		leaf cost:	0
2.27/1.39	
2.27/1.39	
2.27/1.39	
2.27/1.39	Complexity upper bound 2*ar_1 + 2*ar_3 + 2*ar_5 + 210
2.27/1.39	
2.27/1.39	
2.27/1.39	
2.27/1.39	Time: 0.093 sec (SMT: 0.079 sec)
2.27/1.39	
2.27/1.39	
2.27/1.39	----------------------------------------
2.27/1.39	
2.27/1.39	(2)
2.27/1.39	BOUNDS(1, n^1)
2.41/1.42	EOF