/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/output/output_files/bench.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 278 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_random1d_start(v_2, v_max, v_x.0) -> Com_1(eval_random1d_bb0_in(v_2, v_max, v_x.0)) :|: TRUE eval_random1d_bb0_in(v_2, v_max, v_x.0) -> Com_1(eval_random1d_bb1_in(v_2, v_max, 1)) :|: v_max > 0 eval_random1d_bb0_in(v_2, v_max, v_x.0) -> Com_1(eval_random1d_bb3_in(v_2, v_max, v_x.0)) :|: v_max <= 0 eval_random1d_bb1_in(v_2, v_max, v_x.0) -> Com_1(eval_random1d_bb2_in(v_2, v_max, v_x.0)) :|: v_x.0 <= v_max eval_random1d_bb1_in(v_2, v_max, v_x.0) -> Com_1(eval_random1d_bb3_in(v_2, v_max, v_x.0)) :|: v_x.0 > v_max eval_random1d_bb2_in(v_2, v_max, v_x.0) -> Com_1(eval_random1d_0(v_2, v_max, v_x.0)) :|: TRUE eval_random1d_0(v_2, v_max, v_x.0) -> Com_2(eval_nondet_start(v_2, v_max, v_x.0), eval_random1d_1(nondef.0, v_max, v_x.0)) :|: TRUE eval_random1d_1(v_2, v_max, v_x.0) -> Com_1(eval_random1d_bb1_in(v_2, v_max, v_x.0 + 1)) :|: v_2 > 0 eval_random1d_1(v_2, v_max, v_x.0) -> Com_1(eval_random1d_bb1_in(v_2, v_max, v_x.0 + 1)) :|: v_2 <= 0 eval_random1d_bb3_in(v_2, v_max, v_x.0) -> Com_1(eval_random1d_stop(v_2, v_max, v_x.0)) :|: TRUE The start-symbols are:[eval_random1d_start_3] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 42*ar_0 + 91) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ] (Comp: ?, Cost: 1) evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] (Comp: ?, Cost: 1) evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] (Comp: ?, Cost: 1) evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) (Comp: ?, Cost: 1) evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) (Comp: ?, Cost: 1) evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ] (Comp: 1, Cost: 1) evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] (Comp: ?, Cost: 1) evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] (Comp: ?, Cost: 1) evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) (Comp: ?, Cost: 1) evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) (Comp: ?, Cost: 1) evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrandom1dstart) = 2 Pol(evalrandom1dbb0in) = 2 Pol(evalrandom1dbb1in) = 2 Pol(evalrandom1dbb3in) = 1 Pol(evalrandom1dbb2in) = 2 Pol(evalrandom1d0) = 2 Pol(evalrandom1d00) = 0 Pol(evalnondetstart) = 0 Pol(evalrandom1d01) = 2 Pol(evalrandom1d1) = 2 Pol(evalrandom1dstop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3)) evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ] (Comp: 1, Cost: 1) evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] (Comp: ?, Cost: 1) evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] (Comp: 2, Cost: 1) evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) (Comp: ?, Cost: 1) evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) (Comp: ?, Cost: 1) evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ 0 >= ar_2 ] (Comp: 2, Cost: 1) evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalrandom1d0: X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalrandom1d00: X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalrandom1d01: X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalrandom1d1: X_3 - X_4 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalrandom1dbb1in: X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalrandom1dbb2in: X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] (Comp: 1, Cost: 1) evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] (Comp: 1, Cost: 1) evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ] (Comp: 1, Cost: 1) evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrandom1dbb2in) = 6*V_1 - 6*V_2 + 5 Pol(evalrandom1d0) = 6*V_1 - 6*V_2 + 4 Pol(evalrandom1dbb1in) = 6*V_1 - 6*V_2 + 6 Pol(evalrandom1d1) = 6*V_1 - 6*V_2 + 1 Pol(evalrandom1d01) = 6*V_1 - 6*V_2 + 2 Pol(evalrandom1d00) = 1 Pol(evalnondetstart) = 0 and size complexities S("evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 S("evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 S("evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 S("evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-0) = ar_0 S("evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-1) = 1 S("evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-2) = ar_2 S("evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-3) = ar_3 S("evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ar_0 S("evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1 S("evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2 S("evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3 S("evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 ]", 0-0) = ar_0 S("evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 ]", 0-1) = ? S("evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 ]", 0-2) = ? S("evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 ]", 0-3) = ? S("evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-0) = ar_0 S("evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-1) = ? S("evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-2) = ? S("evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-3) = ? S("evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0 S("evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ? S("evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ? S("evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ? S("evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0 S("evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ? S("evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ? S("evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ? S("evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0 S("evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ? S("evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ? S("evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ? S("evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0 S("evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ? S("evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ? S("evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ? S("evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 1-0) = ar_0 S("evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 1-1) = ? S("evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 1-2) = ? S("evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 1-3) = ? S("evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-0) = ar_0 S("evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-1) = ? S("evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-2) = ? S("evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-3) = ? S("evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-0) = ar_0 S("evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-1) = ? S("evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-2) = ? S("evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-3) = ? S("evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ? S("evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? S("evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ? S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3 orients the transitions evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ] evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] weakly and the transitions evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ] evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dstop(ar_0, ar_1, ar_2, ar_3)) (Comp: 6*ar_0 + 12, Cost: 1) evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] (Comp: 6*ar_0 + 12, Cost: 1) evalrandom1d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ] (Comp: 6*ar_0 + 12, Cost: 1) evalrandom1d0(ar_0, ar_1, ar_2, ar_3) -> Com_2(evalrandom1d00(ar_0, ar_1, ar_2, e), evalrandom1d01(ar_0, ar_1, ar_2, e)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 6*ar_0 + 12, Cost: 1) evalrandom1d01(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d1(ar_0, ar_1, ar_3, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 6*ar_0 + 12, Cost: 1) evalrandom1d00(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 6*ar_0 + 12, Cost: 1) evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1d0(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 + 1 ] (Comp: 6*ar_0 + 12, Cost: 1) evalrandom1dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 ] (Comp: 1, Cost: 1) evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] (Comp: 1, Cost: 1) evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 1 ] (Comp: 1, Cost: 1) evalrandom1dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom1dbb0in(ar_0, ar_1, ar_2, ar_3)) start location: koat_start leaf cost: 0 Complexity upper bound 42*ar_0 + 91 Time: 0.280 sec (SMT: 0.227 sec) ---------------------------------------- (2) BOUNDS(1, n^1)