/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files


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MAYBE
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, INF).

(0) CpxIntTrs


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
eval_sipmamergesort_init_start(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb0_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: TRUE
eval_sipmamergesort_init_bb0_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb1_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, 1, v_q.1, v_q.3, v_r.1, v_r.3, 1)) :|: TRUE
eval_sipmamergesort_init_bb1_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb2_in(v_10, v_27, v_6, v_i.5, v_n, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_up.0 < 0
eval_sipmamergesort_init_bb1_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb2_in(v_10, v_27, v_6, v_i.5, v_n, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_up.0 < 0 && v_up.0 > 0
eval_sipmamergesort_init_bb1_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb2_in(v_10, v_27, v_6, v_i.5, v_n, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_up.0 > 0
eval_sipmamergesort_init_bb1_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb2_in(v_10, v_27, v_6, v_i.5, v_n, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_up.0 < 0 && v_up.0 >= 0 && v_up.0 <= 0
eval_sipmamergesort_init_bb1_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb2_in(v_10, v_27, v_6, v_i.5, v_n, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_up.0 < 0 && v_up.0 > 0 && v_up.0 >= 0 && v_up.0 <= 0
eval_sipmamergesort_init_bb1_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb2_in(v_10, v_27, v_6, v_i.5, v_n, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_up.0 > 0 && v_up.0 >= 0 && v_up.0 <= 0
eval_sipmamergesort_init_bb1_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb2_in(v_10, v_27, v_6, v_i.5, v_n, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_up.0 >= 0 && v_up.0 <= 0
eval_sipmamergesort_init_bb2_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb3_in(v_10, v_27, v_m.0 - 2 * v_p.0, v_i.5, v_m.0, v_n, v_p.0, v_p.0, v_q.3, v_p.0, v_r.3, v_up.0)) :|: v_m.0 >= v_p.0 && v_m.0 - v_p.0 >= v_p.0
eval_sipmamergesort_init_bb2_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb3_in(v_10, v_27, 0, v_i.5, v_m.0, v_n, v_p.0, v_p.0, v_q.3, v_m.0 - v_p.0, v_r.3, v_up.0)) :|: v_m.0 >= v_p.0 && v_m.0 - v_p.0 < v_p.0
eval_sipmamergesort_init_bb2_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb3_in(v_10, v_27, -(v_p.0), v_i.5, v_m.0, v_n, v_p.0, v_m.0, v_q.3, v_p.0, v_r.3, v_up.0)) :|: v_m.0 < v_p.0 && 0 >= v_p.0
eval_sipmamergesort_init_bb2_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb3_in(v_10, v_27, 0, v_i.5, v_m.0, v_n, v_p.0, v_m.0, v_q.3, 0, v_r.3, v_up.0)) :|: v_m.0 < v_p.0 && 0 < v_p.0
eval_sipmamergesort_init_bb3_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb4_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_q.1 > 0 && v_r.1 > 0
eval_sipmamergesort_init_bb3_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb7_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.1, v_up.0)) :|: v_q.1 <= 0
eval_sipmamergesort_init_bb3_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb7_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.1, v_up.0)) :|: v_r.1 <= 0
eval_sipmamergesort_init_bb4_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_12(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: TRUE
eval_sipmamergesort_init_12(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_2(eval_nondet_start(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0), eval_sipmamergesort_init_13(nondef.0, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: TRUE
eval_sipmamergesort_init_13(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb5_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_10 < 0
eval_sipmamergesort_init_13(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb5_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_10 > 0
eval_sipmamergesort_init_13(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb6_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_10 >= 0 && v_10 <= 0
eval_sipmamergesort_init_bb5_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb3_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1 - 1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: TRUE
eval_sipmamergesort_init_bb6_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb3_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1 - 1, v_r.3, v_up.0)) :|: TRUE
eval_sipmamergesort_init_bb7_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb8_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_r.3 > 0
eval_sipmamergesort_init_bb7_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb9_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.1, v_r.1, v_r.3, v_up.0)) :|: v_r.3 <= 0
eval_sipmamergesort_init_bb8_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb7_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3 - 1, v_up.0)) :|: TRUE
eval_sipmamergesort_init_bb9_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb10_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_q.3 > 0
eval_sipmamergesort_init_bb9_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb11_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_q.3 <= 0
eval_sipmamergesort_init_bb10_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb9_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3 - 1, v_r.1, v_r.3, v_up.0)) :|: TRUE
eval_sipmamergesort_init_bb11_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb2_in(v_10, v_27, v_6, v_i.5, v_6, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_6 > 0
eval_sipmamergesort_init_bb11_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb12_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_6 <= 0
eval_sipmamergesort_init_bb12_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb1_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, 2 * v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, -(v_up.0) + 1)) :|: 2 * v_p.0 < v_n
eval_sipmamergesort_init_bb12_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb13_in(v_10, -(v_up.0) + 1, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: 2 * v_p.0 >= v_n
eval_sipmamergesort_init_bb13_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb14_in(v_10, v_27, v_6, 1, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_27 >= 0 && v_27 <= 0
eval_sipmamergesort_init_bb13_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb16_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_27 < 0
eval_sipmamergesort_init_bb13_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb16_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_27 > 0
eval_sipmamergesort_init_bb14_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb15_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_i.5 <= v_n
eval_sipmamergesort_init_bb14_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb16_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: v_i.5 > v_n
eval_sipmamergesort_init_bb15_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_bb14_in(v_10, v_27, v_6, v_i.5 + 1, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: TRUE
eval_sipmamergesort_init_bb16_in(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0) -> Com_1(eval_sipmamergesort_init_stop(v_10, v_27, v_6, v_i.5, v_m.0, v_n, v_p.0, v_q.1, v_q.3, v_r.1, v_r.3, v_up.0)) :|: TRUE

The start-symbols are:[eval_sipmamergesort_init_start_12]