/export/starexec/sandbox2/solver/bin/starexec_run_c_complexity /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(1)) proof of /export/starexec/sandbox2/output/output_files/bench.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 272 ms] (2) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.0, v_x) -> Com_1(eval_foo_bb0_in(v_.0, v_x)) :|: TRUE eval_foo_bb0_in(v_.0, v_x) -> Com_1(eval_foo_bb1_in(v_x, v_x)) :|: TRUE eval_foo_bb1_in(v_.0, v_x) -> Com_1(eval_foo_bb2_in(v_.0, v_x)) :|: v_.0 >= 0 eval_foo_bb1_in(v_.0, v_x) -> Com_1(eval_foo_bb3_in(v_.0, v_x)) :|: v_.0 < 0 eval_foo_bb2_in(v_.0, v_x) -> Com_1(eval_foo_bb1_in(-(2) * v_.0 + 10, v_x)) :|: TRUE eval_foo_bb3_in(v_.0, v_x) -> Com_1(eval_foo_stop(v_.0, v_x)) :|: TRUE The start-symbols are:[eval_foo_start_2] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 42) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfoostart(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_1, Ar_1)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb2in(Ar_0, Ar_1)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostart(Ar_0, Ar_1)) [ 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) evalfoostart(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_1, Ar_1)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb2in(Ar_0, Ar_1)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoostart) = 2 Pol(evalfoobb0in) = 2 Pol(evalfoobb1in) = 2 Pol(evalfoobb2in) = 2 Pol(evalfoobb3in) = 1 Pol(evalfoostop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_1, Ar_1)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb2in(Ar_0, Ar_1)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalfoobb2in: X_1 >= 0 For symbol evalfoobb3in: -X_1 - 1 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostart(Ar_0, Ar_1)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) [ -Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb2in(Ar_0, Ar_1)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_1, Ar_1)) (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) start location: koat_start leaf cost: 0 By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(evalfoostart(Ar_0, Ar_1)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained: koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) [ 0 <= 0 ] We thus obtain the following problem: 5: T: (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) [ -Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb2in(Ar_0, Ar_1)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_1, Ar_1)) (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 5: evalfoostart(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) We thus obtain the following problem: 6: T: (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) [ -Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb2in(Ar_0, Ar_1)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_1, Ar_1)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb2in(Ar_0, Ar_1)) [ Ar_0 >= 0 ] with all transitions in problem 6, the following new transition is obtained: evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) [ Ar_0 >= 0 ] We thus obtain the following problem: 7: T: (Comp: ?, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) [ -Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_1, Ar_1)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 7: evalfoobb2in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) [ Ar_0 >= 0 ] We thus obtain the following problem: 8: T: (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) [ -Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_1, Ar_1)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] with all transitions in problem 8, the following new transition is obtained: evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ -Ar_0 - 1 >= 0 ] We thus obtain the following problem: 9: T: (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ -Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) [ -Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_1, Ar_1)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 9: evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) [ -Ar_0 - 1 >= 0 ] We thus obtain the following problem: 10: T: (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ -Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_1, Ar_1)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) [ 0 <= 0 ] with all transitions in problem 10, the following new transition is obtained: koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_1, Ar_1)) [ 0 <= 0 ] We thus obtain the following problem: 11: T: (Comp: 1, Cost: 2) koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_1, Ar_1)) [ 0 <= 0 ] (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ -Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_1, Ar_1)) start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 11: evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_1, Ar_1)) We thus obtain the following problem: 12: T: (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ -Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 2) koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_1, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_1, Ar_1)) [ 0 <= 0 ] with all transitions in problem 12, the following new transitions are obtained: koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_1, Ar_1)) [ 0 <= 0 /\ 0 >= Ar_1 + 1 /\ -Ar_1 - 1 >= 0 ] koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_1 + 10, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 ] We thus obtain the following problem: 13: T: (Comp: 1, Cost: 4) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_1, Ar_1)) [ 0 <= 0 /\ 0 >= Ar_1 + 1 /\ -Ar_1 - 1 >= 0 ] (Comp: 1, Cost: 4) koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_1 + 10, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ -Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) [ Ar_0 >= 0 ] start location: koat_start leaf cost: 0 By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_1 + 10, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 ] with all transitions in problem 13, the following new transitions are obtained: koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(-2*Ar_1 + 10, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ 0 >= -2*Ar_1 + 11 /\ 2*Ar_1 - 11 >= 0 ] koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb1in(4*Ar_1 - 10, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ -2*Ar_1 + 10 >= 0 ] We thus obtain the following problem: 14: T: (Comp: 1, Cost: 6) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(-2*Ar_1 + 10, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ 0 >= -2*Ar_1 + 11 /\ 2*Ar_1 - 11 >= 0 ] (Comp: 1, Cost: 6) koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb1in(4*Ar_1 - 10, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ -2*Ar_1 + 10 >= 0 ] (Comp: 1, Cost: 4) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_1, Ar_1)) [ 0 <= 0 /\ 0 >= Ar_1 + 1 /\ -Ar_1 - 1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ -Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) [ Ar_0 >= 0 ] start location: koat_start leaf cost: 0 By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb1in(4*Ar_1 - 10, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ -2*Ar_1 + 10 >= 0 ] with all transitions in problem 14, the following new transitions are obtained: koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(4*Ar_1 - 10, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ -2*Ar_1 + 10 >= 0 /\ 0 >= 4*Ar_1 - 9 /\ -4*Ar_1 + 9 >= 0 ] koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-8*Ar_1 + 30, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ -2*Ar_1 + 10 >= 0 /\ 4*Ar_1 - 10 >= 0 ] We thus obtain the following problem: 15: T: (Comp: 1, Cost: 8) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(4*Ar_1 - 10, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ -2*Ar_1 + 10 >= 0 /\ 0 >= 4*Ar_1 - 9 /\ -4*Ar_1 + 9 >= 0 ] (Comp: 1, Cost: 8) koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-8*Ar_1 + 30, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ -2*Ar_1 + 10 >= 0 /\ 4*Ar_1 - 10 >= 0 ] (Comp: 1, Cost: 6) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(-2*Ar_1 + 10, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ 0 >= -2*Ar_1 + 11 /\ 2*Ar_1 - 11 >= 0 ] (Comp: 1, Cost: 4) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_1, Ar_1)) [ 0 <= 0 /\ 0 >= Ar_1 + 1 /\ -Ar_1 - 1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ -Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) [ Ar_0 >= 0 ] start location: koat_start leaf cost: 0 By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-8*Ar_1 + 30, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ -2*Ar_1 + 10 >= 0 /\ 4*Ar_1 - 10 >= 0 ] with all transitions in problem 15, the following new transitions are obtained: koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(-8*Ar_1 + 30, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ -2*Ar_1 + 10 >= 0 /\ 4*Ar_1 - 10 >= 0 /\ 0 >= -8*Ar_1 + 31 /\ 8*Ar_1 - 31 >= 0 ] koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb1in(16*Ar_1 - 50, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ -2*Ar_1 + 10 >= 0 /\ 4*Ar_1 - 10 >= 0 /\ -8*Ar_1 + 30 >= 0 ] We thus obtain the following problem: 16: T: (Comp: 1, Cost: 10) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(-8*Ar_1 + 30, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ -2*Ar_1 + 10 >= 0 /\ 4*Ar_1 - 10 >= 0 /\ 0 >= -8*Ar_1 + 31 /\ 8*Ar_1 - 31 >= 0 ] (Comp: 1, Cost: 10) koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb1in(16*Ar_1 - 50, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ -2*Ar_1 + 10 >= 0 /\ 4*Ar_1 - 10 >= 0 /\ -8*Ar_1 + 30 >= 0 ] (Comp: 1, Cost: 8) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(4*Ar_1 - 10, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ -2*Ar_1 + 10 >= 0 /\ 0 >= 4*Ar_1 - 9 /\ -4*Ar_1 + 9 >= 0 ] (Comp: 1, Cost: 6) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(-2*Ar_1 + 10, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ 0 >= -2*Ar_1 + 11 /\ 2*Ar_1 - 11 >= 0 ] (Comp: 1, Cost: 4) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_1, Ar_1)) [ 0 <= 0 /\ 0 >= Ar_1 + 1 /\ -Ar_1 - 1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ -Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) [ Ar_0 >= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 16: evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(-2*Ar_0 + 10, Ar_1)) [ Ar_0 >= 0 ] We thus obtain the following problem: 17: T: (Comp: 2, Cost: 2) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ -Ar_0 - 1 >= 0 ] (Comp: 1, Cost: 10) koat_start(Ar_0, Ar_1) -> Com_1(evalfoobb1in(16*Ar_1 - 50, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ -2*Ar_1 + 10 >= 0 /\ 4*Ar_1 - 10 >= 0 /\ -8*Ar_1 + 30 >= 0 ] (Comp: 1, Cost: 10) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(-8*Ar_1 + 30, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ -2*Ar_1 + 10 >= 0 /\ 4*Ar_1 - 10 >= 0 /\ 0 >= -8*Ar_1 + 31 /\ 8*Ar_1 - 31 >= 0 ] (Comp: 1, Cost: 8) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(4*Ar_1 - 10, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ -2*Ar_1 + 10 >= 0 /\ 0 >= 4*Ar_1 - 9 /\ -4*Ar_1 + 9 >= 0 ] (Comp: 1, Cost: 6) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(-2*Ar_1 + 10, Ar_1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ 0 >= -2*Ar_1 + 11 /\ 2*Ar_1 - 11 >= 0 ] (Comp: 1, Cost: 4) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_1, Ar_1)) [ 0 <= 0 /\ 0 >= Ar_1 + 1 /\ -Ar_1 - 1 >= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 42 Time: 0.295 sec (SMT: 0.266 sec) ---------------------------------------- (2) BOUNDS(1, 1)