MAYBE 1065.48/297.03 MAYBE 1065.48/297.03 1065.48/297.03 We are left with following problem, upon which TcT provides the 1065.48/297.03 certificate MAYBE. 1065.48/297.03 1065.48/297.03 Strict Trs: 1065.48/297.03 { active(from(X)) -> from(active(X)) 1065.48/297.03 , active(from(X)) -> mark(cons(X, from(s(X)))) 1065.48/297.03 , active(cons(X1, X2)) -> cons(active(X1), X2) 1065.48/297.03 , active(s(X)) -> s(active(X)) 1065.48/297.03 , active(after(X1, X2)) -> after(X1, active(X2)) 1065.48/297.03 , active(after(X1, X2)) -> after(active(X1), X2) 1065.48/297.03 , active(after(s(N), cons(X, XS))) -> mark(after(N, XS)) 1065.48/297.03 , active(after(0(), XS)) -> mark(XS) 1065.48/297.03 , from(mark(X)) -> mark(from(X)) 1065.48/297.03 , from(ok(X)) -> ok(from(X)) 1065.48/297.03 , cons(mark(X1), X2) -> mark(cons(X1, X2)) 1065.48/297.03 , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 1065.48/297.03 , s(mark(X)) -> mark(s(X)) 1065.48/297.03 , s(ok(X)) -> ok(s(X)) 1065.48/297.03 , after(X1, mark(X2)) -> mark(after(X1, X2)) 1065.48/297.03 , after(mark(X1), X2) -> mark(after(X1, X2)) 1065.48/297.03 , after(ok(X1), ok(X2)) -> ok(after(X1, X2)) 1065.48/297.03 , proper(from(X)) -> from(proper(X)) 1065.48/297.03 , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 1065.48/297.03 , proper(s(X)) -> s(proper(X)) 1065.48/297.03 , proper(after(X1, X2)) -> after(proper(X1), proper(X2)) 1065.48/297.03 , proper(0()) -> ok(0()) 1065.48/297.03 , top(mark(X)) -> top(proper(X)) 1065.48/297.03 , top(ok(X)) -> top(active(X)) } 1065.48/297.03 Obligation: 1065.48/297.03 runtime complexity 1065.48/297.03 Answer: 1065.48/297.03 MAYBE 1065.48/297.03 1065.48/297.03 None of the processors succeeded. 1065.48/297.03 1065.48/297.03 Details of failed attempt(s): 1065.48/297.03 ----------------------------- 1065.48/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1065.48/297.03 following reason: 1065.48/297.03 1065.48/297.03 Computation stopped due to timeout after 297.0 seconds. 1065.48/297.03 1065.48/297.03 2) 'Best' failed due to the following reason: 1065.48/297.03 1065.48/297.03 None of the processors succeeded. 1065.48/297.03 1065.48/297.03 Details of failed attempt(s): 1065.48/297.03 ----------------------------- 1065.48/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1065.48/297.03 seconds)' failed due to the following reason: 1065.48/297.03 1065.48/297.03 Computation stopped due to timeout after 148.0 seconds. 1065.48/297.03 1065.48/297.03 2) 'Best' failed due to the following reason: 1065.48/297.03 1065.48/297.03 None of the processors succeeded. 1065.48/297.03 1065.48/297.03 Details of failed attempt(s): 1065.48/297.03 ----------------------------- 1065.48/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1065.48/297.03 following reason: 1065.48/297.03 1065.48/297.03 The processor is inapplicable, reason: 1065.48/297.03 Processor only applicable for innermost runtime complexity analysis 1065.48/297.03 1065.48/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1065.48/297.03 to the following reason: 1065.48/297.03 1065.48/297.03 The processor is inapplicable, reason: 1065.48/297.03 Processor only applicable for innermost runtime complexity analysis 1065.48/297.03 1065.48/297.03 1065.48/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1065.48/297.03 failed due to the following reason: 1065.48/297.03 1065.48/297.03 None of the processors succeeded. 1065.48/297.03 1065.48/297.03 Details of failed attempt(s): 1065.48/297.03 ----------------------------- 1065.48/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1065.48/297.03 failed due to the following reason: 1065.48/297.03 1065.48/297.03 match-boundness of the problem could not be verified. 1065.48/297.03 1065.48/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1065.48/297.03 failed due to the following reason: 1065.48/297.03 1065.48/297.03 match-boundness of the problem could not be verified. 1065.48/297.03 1065.48/297.03 1065.48/297.03 1065.48/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1065.48/297.03 the following reason: 1065.48/297.03 1065.48/297.03 We add the following weak dependency pairs: 1065.48/297.03 1065.48/297.03 Strict DPs: 1065.48/297.03 { active^#(from(X)) -> c_1(from^#(active(X))) 1065.48/297.03 , active^#(from(X)) -> c_2(cons^#(X, from(s(X)))) 1065.48/297.03 , active^#(cons(X1, X2)) -> c_3(cons^#(active(X1), X2)) 1065.48/297.03 , active^#(s(X)) -> c_4(s^#(active(X))) 1065.48/297.03 , active^#(after(X1, X2)) -> c_5(after^#(X1, active(X2))) 1065.48/297.03 , active^#(after(X1, X2)) -> c_6(after^#(active(X1), X2)) 1065.48/297.03 , active^#(after(s(N), cons(X, XS))) -> c_7(after^#(N, XS)) 1065.48/297.03 , active^#(after(0(), XS)) -> c_8(XS) 1065.48/297.03 , from^#(mark(X)) -> c_9(from^#(X)) 1065.48/297.03 , from^#(ok(X)) -> c_10(from^#(X)) 1065.48/297.03 , cons^#(mark(X1), X2) -> c_11(cons^#(X1, X2)) 1065.48/297.03 , cons^#(ok(X1), ok(X2)) -> c_12(cons^#(X1, X2)) 1065.48/297.03 , s^#(mark(X)) -> c_13(s^#(X)) 1065.48/297.03 , s^#(ok(X)) -> c_14(s^#(X)) 1065.48/297.03 , after^#(X1, mark(X2)) -> c_15(after^#(X1, X2)) 1065.48/297.03 , after^#(mark(X1), X2) -> c_16(after^#(X1, X2)) 1065.48/297.03 , after^#(ok(X1), ok(X2)) -> c_17(after^#(X1, X2)) 1065.48/297.03 , proper^#(from(X)) -> c_18(from^#(proper(X))) 1065.48/297.03 , proper^#(cons(X1, X2)) -> c_19(cons^#(proper(X1), proper(X2))) 1065.48/297.03 , proper^#(s(X)) -> c_20(s^#(proper(X))) 1065.48/297.03 , proper^#(after(X1, X2)) -> c_21(after^#(proper(X1), proper(X2))) 1065.48/297.03 , proper^#(0()) -> c_22() 1065.48/297.03 , top^#(mark(X)) -> c_23(top^#(proper(X))) 1065.48/297.03 , top^#(ok(X)) -> c_24(top^#(active(X))) } 1065.48/297.03 1065.48/297.03 and mark the set of starting terms. 1065.48/297.03 1065.48/297.03 We are left with following problem, upon which TcT provides the 1065.48/297.03 certificate MAYBE. 1065.48/297.03 1065.48/297.03 Strict DPs: 1065.48/297.03 { active^#(from(X)) -> c_1(from^#(active(X))) 1065.48/297.03 , active^#(from(X)) -> c_2(cons^#(X, from(s(X)))) 1065.48/297.03 , active^#(cons(X1, X2)) -> c_3(cons^#(active(X1), X2)) 1065.48/297.03 , active^#(s(X)) -> c_4(s^#(active(X))) 1065.48/297.03 , active^#(after(X1, X2)) -> c_5(after^#(X1, active(X2))) 1065.48/297.03 , active^#(after(X1, X2)) -> c_6(after^#(active(X1), X2)) 1065.48/297.03 , active^#(after(s(N), cons(X, XS))) -> c_7(after^#(N, XS)) 1065.48/297.03 , active^#(after(0(), XS)) -> c_8(XS) 1065.48/297.03 , from^#(mark(X)) -> c_9(from^#(X)) 1065.48/297.03 , from^#(ok(X)) -> c_10(from^#(X)) 1065.48/297.03 , cons^#(mark(X1), X2) -> c_11(cons^#(X1, X2)) 1065.48/297.03 , cons^#(ok(X1), ok(X2)) -> c_12(cons^#(X1, X2)) 1065.48/297.03 , s^#(mark(X)) -> c_13(s^#(X)) 1065.48/297.03 , s^#(ok(X)) -> c_14(s^#(X)) 1065.48/297.03 , after^#(X1, mark(X2)) -> c_15(after^#(X1, X2)) 1065.48/297.03 , after^#(mark(X1), X2) -> c_16(after^#(X1, X2)) 1065.48/297.03 , after^#(ok(X1), ok(X2)) -> c_17(after^#(X1, X2)) 1065.48/297.03 , proper^#(from(X)) -> c_18(from^#(proper(X))) 1065.48/297.03 , proper^#(cons(X1, X2)) -> c_19(cons^#(proper(X1), proper(X2))) 1065.48/297.03 , proper^#(s(X)) -> c_20(s^#(proper(X))) 1065.48/297.03 , proper^#(after(X1, X2)) -> c_21(after^#(proper(X1), proper(X2))) 1065.48/297.03 , proper^#(0()) -> c_22() 1065.48/297.03 , top^#(mark(X)) -> c_23(top^#(proper(X))) 1065.48/297.03 , top^#(ok(X)) -> c_24(top^#(active(X))) } 1065.48/297.03 Strict Trs: 1065.48/297.03 { active(from(X)) -> from(active(X)) 1065.48/297.03 , active(from(X)) -> mark(cons(X, from(s(X)))) 1065.48/297.03 , active(cons(X1, X2)) -> cons(active(X1), X2) 1065.48/297.03 , active(s(X)) -> s(active(X)) 1065.48/297.03 , active(after(X1, X2)) -> after(X1, active(X2)) 1065.48/297.03 , active(after(X1, X2)) -> after(active(X1), X2) 1065.48/297.03 , active(after(s(N), cons(X, XS))) -> mark(after(N, XS)) 1065.48/297.03 , active(after(0(), XS)) -> mark(XS) 1065.48/297.03 , from(mark(X)) -> mark(from(X)) 1065.48/297.03 , from(ok(X)) -> ok(from(X)) 1065.48/297.03 , cons(mark(X1), X2) -> mark(cons(X1, X2)) 1065.48/297.03 , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 1065.48/297.03 , s(mark(X)) -> mark(s(X)) 1065.48/297.03 , s(ok(X)) -> ok(s(X)) 1065.48/297.03 , after(X1, mark(X2)) -> mark(after(X1, X2)) 1065.48/297.03 , after(mark(X1), X2) -> mark(after(X1, X2)) 1065.48/297.03 , after(ok(X1), ok(X2)) -> ok(after(X1, X2)) 1065.48/297.03 , proper(from(X)) -> from(proper(X)) 1065.48/297.03 , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 1065.48/297.03 , proper(s(X)) -> s(proper(X)) 1065.48/297.03 , proper(after(X1, X2)) -> after(proper(X1), proper(X2)) 1065.48/297.03 , proper(0()) -> ok(0()) 1065.48/297.03 , top(mark(X)) -> top(proper(X)) 1065.48/297.03 , top(ok(X)) -> top(active(X)) } 1065.48/297.03 Obligation: 1065.48/297.03 runtime complexity 1065.48/297.03 Answer: 1065.48/297.03 MAYBE 1065.48/297.03 1065.48/297.03 Consider the dependency graph: 1065.48/297.03 1065.48/297.03 1: active^#(from(X)) -> c_1(from^#(active(X))) 1065.48/297.03 -->_1 from^#(ok(X)) -> c_10(from^#(X)) :10 1065.48/297.03 -->_1 from^#(mark(X)) -> c_9(from^#(X)) :9 1065.48/297.03 1065.48/297.03 2: active^#(from(X)) -> c_2(cons^#(X, from(s(X)))) 1065.48/297.03 -->_1 cons^#(ok(X1), ok(X2)) -> c_12(cons^#(X1, X2)) :12 1065.48/297.03 -->_1 cons^#(mark(X1), X2) -> c_11(cons^#(X1, X2)) :11 1065.48/297.03 1065.48/297.03 3: active^#(cons(X1, X2)) -> c_3(cons^#(active(X1), X2)) 1065.48/297.03 -->_1 cons^#(ok(X1), ok(X2)) -> c_12(cons^#(X1, X2)) :12 1065.48/297.03 -->_1 cons^#(mark(X1), X2) -> c_11(cons^#(X1, X2)) :11 1065.48/297.03 1065.48/297.03 4: active^#(s(X)) -> c_4(s^#(active(X))) 1065.48/297.03 -->_1 s^#(ok(X)) -> c_14(s^#(X)) :14 1065.48/297.03 -->_1 s^#(mark(X)) -> c_13(s^#(X)) :13 1065.48/297.03 1065.48/297.03 5: active^#(after(X1, X2)) -> c_5(after^#(X1, active(X2))) 1065.48/297.03 -->_1 after^#(ok(X1), ok(X2)) -> c_17(after^#(X1, X2)) :17 1065.48/297.03 -->_1 after^#(mark(X1), X2) -> c_16(after^#(X1, X2)) :16 1065.48/297.03 -->_1 after^#(X1, mark(X2)) -> c_15(after^#(X1, X2)) :15 1065.48/297.03 1065.48/297.03 6: active^#(after(X1, X2)) -> c_6(after^#(active(X1), X2)) 1065.48/297.03 -->_1 after^#(ok(X1), ok(X2)) -> c_17(after^#(X1, X2)) :17 1065.48/297.04 -->_1 after^#(mark(X1), X2) -> c_16(after^#(X1, X2)) :16 1065.48/297.04 -->_1 after^#(X1, mark(X2)) -> c_15(after^#(X1, X2)) :15 1065.48/297.04 1065.48/297.04 7: active^#(after(s(N), cons(X, XS))) -> c_7(after^#(N, XS)) 1065.48/297.04 -->_1 after^#(ok(X1), ok(X2)) -> c_17(after^#(X1, X2)) :17 1065.48/297.04 -->_1 after^#(mark(X1), X2) -> c_16(after^#(X1, X2)) :16 1065.48/297.04 -->_1 after^#(X1, mark(X2)) -> c_15(after^#(X1, X2)) :15 1065.48/297.04 1065.48/297.04 8: active^#(after(0(), XS)) -> c_8(XS) 1065.48/297.04 -->_1 top^#(ok(X)) -> c_24(top^#(active(X))) :24 1065.48/297.04 -->_1 top^#(mark(X)) -> c_23(top^#(proper(X))) :23 1065.48/297.04 -->_1 proper^#(after(X1, X2)) -> 1065.48/297.04 c_21(after^#(proper(X1), proper(X2))) :21 1065.48/297.04 -->_1 proper^#(s(X)) -> c_20(s^#(proper(X))) :20 1065.48/297.04 -->_1 proper^#(cons(X1, X2)) -> 1065.48/297.04 c_19(cons^#(proper(X1), proper(X2))) :19 1065.48/297.04 -->_1 proper^#(from(X)) -> c_18(from^#(proper(X))) :18 1065.48/297.04 -->_1 after^#(ok(X1), ok(X2)) -> c_17(after^#(X1, X2)) :17 1065.48/297.04 -->_1 after^#(mark(X1), X2) -> c_16(after^#(X1, X2)) :16 1065.48/297.04 -->_1 after^#(X1, mark(X2)) -> c_15(after^#(X1, X2)) :15 1065.48/297.04 -->_1 s^#(ok(X)) -> c_14(s^#(X)) :14 1065.48/297.04 -->_1 s^#(mark(X)) -> c_13(s^#(X)) :13 1065.48/297.04 -->_1 cons^#(ok(X1), ok(X2)) -> c_12(cons^#(X1, X2)) :12 1065.48/297.04 -->_1 cons^#(mark(X1), X2) -> c_11(cons^#(X1, X2)) :11 1065.48/297.04 -->_1 from^#(ok(X)) -> c_10(from^#(X)) :10 1065.48/297.04 -->_1 from^#(mark(X)) -> c_9(from^#(X)) :9 1065.48/297.04 -->_1 proper^#(0()) -> c_22() :22 1065.48/297.04 -->_1 active^#(after(0(), XS)) -> c_8(XS) :8 1065.48/297.04 -->_1 active^#(after(s(N), cons(X, XS))) -> c_7(after^#(N, XS)) :7 1065.48/297.04 -->_1 active^#(after(X1, X2)) -> c_6(after^#(active(X1), X2)) :6 1065.48/297.04 -->_1 active^#(after(X1, X2)) -> c_5(after^#(X1, active(X2))) :5 1065.48/297.04 -->_1 active^#(s(X)) -> c_4(s^#(active(X))) :4 1065.48/297.04 -->_1 active^#(cons(X1, X2)) -> c_3(cons^#(active(X1), X2)) :3 1065.48/297.04 -->_1 active^#(from(X)) -> c_2(cons^#(X, from(s(X)))) :2 1065.48/297.04 -->_1 active^#(from(X)) -> c_1(from^#(active(X))) :1 1065.48/297.04 1065.48/297.04 9: from^#(mark(X)) -> c_9(from^#(X)) 1065.48/297.04 -->_1 from^#(ok(X)) -> c_10(from^#(X)) :10 1065.48/297.04 -->_1 from^#(mark(X)) -> c_9(from^#(X)) :9 1065.48/297.04 1065.48/297.04 10: from^#(ok(X)) -> c_10(from^#(X)) 1065.48/297.04 -->_1 from^#(ok(X)) -> c_10(from^#(X)) :10 1065.48/297.04 -->_1 from^#(mark(X)) -> c_9(from^#(X)) :9 1065.48/297.04 1065.48/297.04 11: cons^#(mark(X1), X2) -> c_11(cons^#(X1, X2)) 1065.48/297.04 -->_1 cons^#(ok(X1), ok(X2)) -> c_12(cons^#(X1, X2)) :12 1065.48/297.04 -->_1 cons^#(mark(X1), X2) -> c_11(cons^#(X1, X2)) :11 1065.48/297.04 1065.48/297.04 12: cons^#(ok(X1), ok(X2)) -> c_12(cons^#(X1, X2)) 1065.48/297.04 -->_1 cons^#(ok(X1), ok(X2)) -> c_12(cons^#(X1, X2)) :12 1065.48/297.04 -->_1 cons^#(mark(X1), X2) -> c_11(cons^#(X1, X2)) :11 1065.48/297.04 1065.48/297.04 13: s^#(mark(X)) -> c_13(s^#(X)) 1065.48/297.04 -->_1 s^#(ok(X)) -> c_14(s^#(X)) :14 1065.48/297.04 -->_1 s^#(mark(X)) -> c_13(s^#(X)) :13 1065.48/297.04 1065.48/297.04 14: s^#(ok(X)) -> c_14(s^#(X)) 1065.48/297.04 -->_1 s^#(ok(X)) -> c_14(s^#(X)) :14 1065.48/297.04 -->_1 s^#(mark(X)) -> c_13(s^#(X)) :13 1065.48/297.04 1065.48/297.04 15: after^#(X1, mark(X2)) -> c_15(after^#(X1, X2)) 1065.48/297.04 -->_1 after^#(ok(X1), ok(X2)) -> c_17(after^#(X1, X2)) :17 1065.48/297.04 -->_1 after^#(mark(X1), X2) -> c_16(after^#(X1, X2)) :16 1065.48/297.04 -->_1 after^#(X1, mark(X2)) -> c_15(after^#(X1, X2)) :15 1065.48/297.04 1065.48/297.04 16: after^#(mark(X1), X2) -> c_16(after^#(X1, X2)) 1065.48/297.04 -->_1 after^#(ok(X1), ok(X2)) -> c_17(after^#(X1, X2)) :17 1065.48/297.04 -->_1 after^#(mark(X1), X2) -> c_16(after^#(X1, X2)) :16 1065.48/297.04 -->_1 after^#(X1, mark(X2)) -> c_15(after^#(X1, X2)) :15 1065.48/297.04 1065.48/297.04 17: after^#(ok(X1), ok(X2)) -> c_17(after^#(X1, X2)) 1065.48/297.04 -->_1 after^#(ok(X1), ok(X2)) -> c_17(after^#(X1, X2)) :17 1065.48/297.04 -->_1 after^#(mark(X1), X2) -> c_16(after^#(X1, X2)) :16 1065.48/297.04 -->_1 after^#(X1, mark(X2)) -> c_15(after^#(X1, X2)) :15 1065.48/297.04 1065.48/297.04 18: proper^#(from(X)) -> c_18(from^#(proper(X))) 1065.48/297.04 -->_1 from^#(ok(X)) -> c_10(from^#(X)) :10 1065.48/297.04 -->_1 from^#(mark(X)) -> c_9(from^#(X)) :9 1065.48/297.04 1065.48/297.04 19: proper^#(cons(X1, X2)) -> c_19(cons^#(proper(X1), proper(X2))) 1065.48/297.04 -->_1 cons^#(ok(X1), ok(X2)) -> c_12(cons^#(X1, X2)) :12 1065.48/297.04 -->_1 cons^#(mark(X1), X2) -> c_11(cons^#(X1, X2)) :11 1065.48/297.04 1065.48/297.04 20: proper^#(s(X)) -> c_20(s^#(proper(X))) 1065.48/297.04 -->_1 s^#(ok(X)) -> c_14(s^#(X)) :14 1065.48/297.04 -->_1 s^#(mark(X)) -> c_13(s^#(X)) :13 1065.48/297.04 1065.48/297.04 21: proper^#(after(X1, X2)) -> 1065.48/297.04 c_21(after^#(proper(X1), proper(X2))) 1065.48/297.04 -->_1 after^#(ok(X1), ok(X2)) -> c_17(after^#(X1, X2)) :17 1065.48/297.04 -->_1 after^#(mark(X1), X2) -> c_16(after^#(X1, X2)) :16 1065.48/297.04 -->_1 after^#(X1, mark(X2)) -> c_15(after^#(X1, X2)) :15 1065.48/297.04 1065.48/297.04 22: proper^#(0()) -> c_22() 1065.48/297.04 1065.48/297.04 23: top^#(mark(X)) -> c_23(top^#(proper(X))) 1065.48/297.04 -->_1 top^#(ok(X)) -> c_24(top^#(active(X))) :24 1065.48/297.04 -->_1 top^#(mark(X)) -> c_23(top^#(proper(X))) :23 1065.48/297.04 1065.48/297.04 24: top^#(ok(X)) -> c_24(top^#(active(X))) 1065.48/297.04 -->_1 top^#(ok(X)) -> c_24(top^#(active(X))) :24 1065.48/297.04 -->_1 top^#(mark(X)) -> c_23(top^#(proper(X))) :23 1065.48/297.04 1065.48/297.04 1065.48/297.04 Only the nodes {9,10,11,12,13,14,15,17,16,22,23,24} are reachable 1065.48/297.04 from nodes {9,10,11,12,13,14,15,16,17,22,23,24} that start 1065.48/297.04 derivation from marked basic terms. The nodes not reachable are 1065.48/297.04 removed from the problem. 1065.48/297.04 1065.48/297.04 We are left with following problem, upon which TcT provides the 1065.48/297.04 certificate MAYBE. 1065.48/297.04 1065.48/297.04 Strict DPs: 1065.48/297.04 { from^#(mark(X)) -> c_9(from^#(X)) 1065.48/297.04 , from^#(ok(X)) -> c_10(from^#(X)) 1065.48/297.04 , cons^#(mark(X1), X2) -> c_11(cons^#(X1, X2)) 1065.48/297.04 , cons^#(ok(X1), ok(X2)) -> c_12(cons^#(X1, X2)) 1065.48/297.04 , s^#(mark(X)) -> c_13(s^#(X)) 1065.48/297.04 , s^#(ok(X)) -> c_14(s^#(X)) 1065.48/297.04 , after^#(X1, mark(X2)) -> c_15(after^#(X1, X2)) 1065.48/297.04 , after^#(mark(X1), X2) -> c_16(after^#(X1, X2)) 1065.48/297.04 , after^#(ok(X1), ok(X2)) -> c_17(after^#(X1, X2)) 1065.48/297.04 , proper^#(0()) -> c_22() 1065.48/297.04 , top^#(mark(X)) -> c_23(top^#(proper(X))) 1065.48/297.04 , top^#(ok(X)) -> c_24(top^#(active(X))) } 1065.48/297.04 Strict Trs: 1065.48/297.04 { active(from(X)) -> from(active(X)) 1065.48/297.04 , active(from(X)) -> mark(cons(X, from(s(X)))) 1065.48/297.04 , active(cons(X1, X2)) -> cons(active(X1), X2) 1065.48/297.04 , active(s(X)) -> s(active(X)) 1065.48/297.04 , active(after(X1, X2)) -> after(X1, active(X2)) 1065.48/297.04 , active(after(X1, X2)) -> after(active(X1), X2) 1065.48/297.04 , active(after(s(N), cons(X, XS))) -> mark(after(N, XS)) 1065.48/297.04 , active(after(0(), XS)) -> mark(XS) 1065.48/297.04 , from(mark(X)) -> mark(from(X)) 1065.48/297.04 , from(ok(X)) -> ok(from(X)) 1065.48/297.04 , cons(mark(X1), X2) -> mark(cons(X1, X2)) 1065.48/297.04 , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 1065.48/297.04 , s(mark(X)) -> mark(s(X)) 1065.48/297.04 , s(ok(X)) -> ok(s(X)) 1065.48/297.04 , after(X1, mark(X2)) -> mark(after(X1, X2)) 1065.48/297.04 , after(mark(X1), X2) -> mark(after(X1, X2)) 1065.48/297.04 , after(ok(X1), ok(X2)) -> ok(after(X1, X2)) 1065.48/297.04 , proper(from(X)) -> from(proper(X)) 1065.48/297.04 , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 1065.48/297.04 , proper(s(X)) -> s(proper(X)) 1065.48/297.04 , proper(after(X1, X2)) -> after(proper(X1), proper(X2)) 1065.48/297.04 , proper(0()) -> ok(0()) 1065.48/297.04 , top(mark(X)) -> top(proper(X)) 1065.48/297.04 , top(ok(X)) -> top(active(X)) } 1065.48/297.04 Obligation: 1065.48/297.04 runtime complexity 1065.48/297.04 Answer: 1065.48/297.04 MAYBE 1065.48/297.04 1065.48/297.04 We estimate the number of application of {10} by applications of 1065.48/297.04 Pre({10}) = {}. Here rules are labeled as follows: 1065.48/297.04 1065.48/297.04 DPs: 1065.48/297.04 { 1: from^#(mark(X)) -> c_9(from^#(X)) 1065.48/297.04 , 2: from^#(ok(X)) -> c_10(from^#(X)) 1065.48/297.04 , 3: cons^#(mark(X1), X2) -> c_11(cons^#(X1, X2)) 1065.48/297.04 , 4: cons^#(ok(X1), ok(X2)) -> c_12(cons^#(X1, X2)) 1065.48/297.04 , 5: s^#(mark(X)) -> c_13(s^#(X)) 1065.48/297.04 , 6: s^#(ok(X)) -> c_14(s^#(X)) 1065.48/297.04 , 7: after^#(X1, mark(X2)) -> c_15(after^#(X1, X2)) 1065.48/297.04 , 8: after^#(mark(X1), X2) -> c_16(after^#(X1, X2)) 1065.48/297.04 , 9: after^#(ok(X1), ok(X2)) -> c_17(after^#(X1, X2)) 1065.48/297.04 , 10: proper^#(0()) -> c_22() 1065.48/297.04 , 11: top^#(mark(X)) -> c_23(top^#(proper(X))) 1065.48/297.04 , 12: top^#(ok(X)) -> c_24(top^#(active(X))) } 1065.48/297.04 1065.48/297.04 We are left with following problem, upon which TcT provides the 1065.48/297.04 certificate MAYBE. 1065.48/297.04 1065.48/297.04 Strict DPs: 1065.48/297.04 { from^#(mark(X)) -> c_9(from^#(X)) 1065.48/297.04 , from^#(ok(X)) -> c_10(from^#(X)) 1065.48/297.04 , cons^#(mark(X1), X2) -> c_11(cons^#(X1, X2)) 1065.48/297.04 , cons^#(ok(X1), ok(X2)) -> c_12(cons^#(X1, X2)) 1065.48/297.04 , s^#(mark(X)) -> c_13(s^#(X)) 1065.48/297.04 , s^#(ok(X)) -> c_14(s^#(X)) 1065.48/297.04 , after^#(X1, mark(X2)) -> c_15(after^#(X1, X2)) 1065.48/297.04 , after^#(mark(X1), X2) -> c_16(after^#(X1, X2)) 1065.48/297.04 , after^#(ok(X1), ok(X2)) -> c_17(after^#(X1, X2)) 1065.48/297.04 , top^#(mark(X)) -> c_23(top^#(proper(X))) 1065.48/297.04 , top^#(ok(X)) -> c_24(top^#(active(X))) } 1065.48/297.04 Strict Trs: 1065.48/297.04 { active(from(X)) -> from(active(X)) 1065.48/297.04 , active(from(X)) -> mark(cons(X, from(s(X)))) 1065.48/297.04 , active(cons(X1, X2)) -> cons(active(X1), X2) 1065.48/297.04 , active(s(X)) -> s(active(X)) 1065.48/297.04 , active(after(X1, X2)) -> after(X1, active(X2)) 1065.48/297.04 , active(after(X1, X2)) -> after(active(X1), X2) 1065.48/297.04 , active(after(s(N), cons(X, XS))) -> mark(after(N, XS)) 1065.48/297.04 , active(after(0(), XS)) -> mark(XS) 1065.48/297.04 , from(mark(X)) -> mark(from(X)) 1065.48/297.04 , from(ok(X)) -> ok(from(X)) 1065.48/297.04 , cons(mark(X1), X2) -> mark(cons(X1, X2)) 1065.48/297.04 , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 1065.48/297.04 , s(mark(X)) -> mark(s(X)) 1065.48/297.04 , s(ok(X)) -> ok(s(X)) 1065.48/297.04 , after(X1, mark(X2)) -> mark(after(X1, X2)) 1065.48/297.04 , after(mark(X1), X2) -> mark(after(X1, X2)) 1065.48/297.04 , after(ok(X1), ok(X2)) -> ok(after(X1, X2)) 1065.48/297.04 , proper(from(X)) -> from(proper(X)) 1065.48/297.04 , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 1065.48/297.04 , proper(s(X)) -> s(proper(X)) 1065.48/297.04 , proper(after(X1, X2)) -> after(proper(X1), proper(X2)) 1065.48/297.04 , proper(0()) -> ok(0()) 1065.48/297.04 , top(mark(X)) -> top(proper(X)) 1065.48/297.04 , top(ok(X)) -> top(active(X)) } 1065.48/297.04 Weak DPs: { proper^#(0()) -> c_22() } 1065.48/297.04 Obligation: 1065.48/297.04 runtime complexity 1065.48/297.04 Answer: 1065.48/297.04 MAYBE 1065.48/297.04 1065.48/297.04 Empty strict component of the problem is NOT empty. 1065.48/297.04 1065.48/297.04 1065.48/297.04 Arrrr.. 1065.76/297.23 EOF