MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { from(X) -> cons(X, from(s(X))) , sel(s(N), cons(X, XS)) -> sel(N, XS) , sel(0(), cons(X, XS)) -> X , minus(X, 0()) -> 0() , minus(s(X), s(Y)) -> minus(X, Y) , quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) , quot(0(), s(Y)) -> 0() , zWquot(XS, nil()) -> nil() , zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), zWquot(XS, YS)) , zWquot(nil(), XS) -> nil() } Obligation: innermost runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 30.0 seconds. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The input cannot be shown compatible 2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The input cannot be shown compatible 3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: We add the following innermost weak dependency pairs: Strict DPs: { from^#(X) -> c_1(from^#(s(X))) , sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) , sel^#(0(), cons(X, XS)) -> c_3() , minus^#(X, 0()) -> c_4() , minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y)) , quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y))) , quot^#(0(), s(Y)) -> c_7() , zWquot^#(XS, nil()) -> c_8() , zWquot^#(cons(X, XS), cons(Y, YS)) -> c_9(quot^#(X, Y), zWquot^#(XS, YS)) , zWquot^#(nil(), XS) -> c_10() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(from^#(s(X))) , sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) , sel^#(0(), cons(X, XS)) -> c_3() , minus^#(X, 0()) -> c_4() , minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y)) , quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y))) , quot^#(0(), s(Y)) -> c_7() , zWquot^#(XS, nil()) -> c_8() , zWquot^#(cons(X, XS), cons(Y, YS)) -> c_9(quot^#(X, Y), zWquot^#(XS, YS)) , zWquot^#(nil(), XS) -> c_10() } Strict Trs: { from(X) -> cons(X, from(s(X))) , sel(s(N), cons(X, XS)) -> sel(N, XS) , sel(0(), cons(X, XS)) -> X , minus(X, 0()) -> 0() , minus(s(X), s(Y)) -> minus(X, Y) , quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) , quot(0(), s(Y)) -> 0() , zWquot(XS, nil()) -> nil() , zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), zWquot(XS, YS)) , zWquot(nil(), XS) -> nil() } Obligation: innermost runtime complexity Answer: MAYBE We replace rewrite rules by usable rules: Strict Usable Rules: { minus(X, 0()) -> 0() , minus(s(X), s(Y)) -> minus(X, Y) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(from^#(s(X))) , sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) , sel^#(0(), cons(X, XS)) -> c_3() , minus^#(X, 0()) -> c_4() , minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y)) , quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y))) , quot^#(0(), s(Y)) -> c_7() , zWquot^#(XS, nil()) -> c_8() , zWquot^#(cons(X, XS), cons(Y, YS)) -> c_9(quot^#(X, Y), zWquot^#(XS, YS)) , zWquot^#(nil(), XS) -> c_10() } Strict Trs: { minus(X, 0()) -> 0() , minus(s(X), s(Y)) -> minus(X, Y) } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following constant growth matrix-interpretation) The following argument positions are usable: Uargs(c_1) = {1}, Uargs(c_2) = {1}, Uargs(c_5) = {1}, Uargs(quot^#) = {1}, Uargs(c_6) = {1}, Uargs(c_9) = {1, 2} TcT has computed the following constructor-restricted matrix interpretation. [cons](x1, x2) = [1 2] x1 + [1 0] x2 + [0] [0 0] [0 0] [0] [s](x1) = [0 0] x1 + [2] [0 1] [2] [0] = [0] [0] [minus](x1, x2) = [0 1] x1 + [1] [0 0] [0] [nil] = [0] [0] [from^#](x1) = [2 0] x1 + [2] [1 1] [2] [c_1](x1) = [1 0] x1 + [1] [0 1] [1] [sel^#](x1, x2) = [0 0] x1 + [0 0] x2 + [2] [1 2] [2 2] [1] [c_2](x1) = [1 0] x1 + [1] [0 1] [1] [c_3] = [1] [1] [minus^#](x1, x2) = [0 0] x1 + [0 0] x2 + [2] [0 1] [1 1] [1] [c_4] = [1] [1] [c_5](x1) = [1 0] x1 + [1] [0 1] [1] [quot^#](x1, x2) = [1 1] x1 + [0] [0 0] [0] [c_6](x1) = [1 0] x1 + [1] [0 1] [2] [c_7] = [2] [0] [zWquot^#](x1, x2) = [2 0] x1 + [0] [0 0] [0] [c_8] = [1] [0] [c_9](x1, x2) = [1 0] x1 + [1 0] x2 + [2] [0 1] [0 1] [2] [c_10] = [1] [0] The following symbols are considered usable {minus, from^#, sel^#, minus^#, quot^#, zWquot^#} The order satisfies the following ordering constraints: [minus(X, 0())] = [0 1] X + [1] [0 0] [0] > [0] [0] = [0()] [minus(s(X), s(Y))] = [0 1] X + [3] [0 0] [0] > [0 1] X + [1] [0 0] [0] = [minus(X, Y)] [from^#(X)] = [2 0] X + [2] [1 1] [2] ? [0 0] X + [7] [0 1] [7] = [c_1(from^#(s(X)))] [sel^#(s(N), cons(X, XS))] = [0 0] X + [0 0] XS + [0 0] N + [2] [2 4] [2 0] [0 2] [7] ? [0 0] XS + [0 0] N + [3] [2 2] [1 2] [2] = [c_2(sel^#(N, XS))] [sel^#(0(), cons(X, XS))] = [0 0] X + [0 0] XS + [2] [2 4] [2 0] [1] > [1] [1] = [c_3()] [minus^#(X, 0())] = [0 0] X + [2] [0 1] [1] > [1] [1] = [c_4()] [minus^#(s(X), s(Y))] = [0 0] X + [0 0] Y + [2] [0 1] [0 1] [7] ? [0 0] X + [0 0] Y + [3] [0 1] [1 1] [2] = [c_5(minus^#(X, Y))] [quot^#(s(X), s(Y))] = [0 1] X + [4] [0 0] [0] ? [0 1] X + [2] [0 0] [2] = [c_6(quot^#(minus(X, Y), s(Y)))] [quot^#(0(), s(Y))] = [0] [0] ? [2] [0] = [c_7()] [zWquot^#(XS, nil())] = [2 0] XS + [0] [0 0] [0] ? [1] [0] = [c_8()] [zWquot^#(cons(X, XS), cons(Y, YS))] = [2 4] X + [2 0] XS + [0] [0 0] [0 0] [0] ? [1 1] X + [2 0] XS + [2] [0 0] [0 0] [2] = [c_9(quot^#(X, Y), zWquot^#(XS, YS))] [zWquot^#(nil(), XS)] = [0] [0] ? [1] [0] = [c_10()] Further, it can be verified that all rules not oriented are covered by the weightgap condition. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(from^#(s(X))) , sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) , minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y)) , quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y))) , quot^#(0(), s(Y)) -> c_7() , zWquot^#(XS, nil()) -> c_8() , zWquot^#(cons(X, XS), cons(Y, YS)) -> c_9(quot^#(X, Y), zWquot^#(XS, YS)) , zWquot^#(nil(), XS) -> c_10() } Weak DPs: { sel^#(0(), cons(X, XS)) -> c_3() , minus^#(X, 0()) -> c_4() } Weak Trs: { minus(X, 0()) -> 0() , minus(s(X), s(Y)) -> minus(X, Y) } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {5,6,8} by applications of Pre({5,6,8}) = {4,7}. Here rules are labeled as follows: DPs: { 1: from^#(X) -> c_1(from^#(s(X))) , 2: sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) , 3: minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y)) , 4: quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y))) , 5: quot^#(0(), s(Y)) -> c_7() , 6: zWquot^#(XS, nil()) -> c_8() , 7: zWquot^#(cons(X, XS), cons(Y, YS)) -> c_9(quot^#(X, Y), zWquot^#(XS, YS)) , 8: zWquot^#(nil(), XS) -> c_10() , 9: sel^#(0(), cons(X, XS)) -> c_3() , 10: minus^#(X, 0()) -> c_4() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(from^#(s(X))) , sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) , minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y)) , quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y))) , zWquot^#(cons(X, XS), cons(Y, YS)) -> c_9(quot^#(X, Y), zWquot^#(XS, YS)) } Weak DPs: { sel^#(0(), cons(X, XS)) -> c_3() , minus^#(X, 0()) -> c_4() , quot^#(0(), s(Y)) -> c_7() , zWquot^#(XS, nil()) -> c_8() , zWquot^#(nil(), XS) -> c_10() } Weak Trs: { minus(X, 0()) -> 0() , minus(s(X), s(Y)) -> minus(X, Y) } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {4} by applications of Pre({4}) = {5}. Here rules are labeled as follows: DPs: { 1: from^#(X) -> c_1(from^#(s(X))) , 2: sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) , 3: minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y)) , 4: quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y))) , 5: zWquot^#(cons(X, XS), cons(Y, YS)) -> c_9(quot^#(X, Y), zWquot^#(XS, YS)) , 6: sel^#(0(), cons(X, XS)) -> c_3() , 7: minus^#(X, 0()) -> c_4() , 8: quot^#(0(), s(Y)) -> c_7() , 9: zWquot^#(XS, nil()) -> c_8() , 10: zWquot^#(nil(), XS) -> c_10() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(from^#(s(X))) , sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) , minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y)) , zWquot^#(cons(X, XS), cons(Y, YS)) -> c_9(quot^#(X, Y), zWquot^#(XS, YS)) } Weak DPs: { sel^#(0(), cons(X, XS)) -> c_3() , minus^#(X, 0()) -> c_4() , quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y))) , quot^#(0(), s(Y)) -> c_7() , zWquot^#(XS, nil()) -> c_8() , zWquot^#(nil(), XS) -> c_10() } Weak Trs: { minus(X, 0()) -> 0() , minus(s(X), s(Y)) -> minus(X, Y) } Obligation: innermost runtime complexity Answer: MAYBE The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. { sel^#(0(), cons(X, XS)) -> c_3() , minus^#(X, 0()) -> c_4() , quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y))) , quot^#(0(), s(Y)) -> c_7() , zWquot^#(XS, nil()) -> c_8() , zWquot^#(nil(), XS) -> c_10() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(from^#(s(X))) , sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) , minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y)) , zWquot^#(cons(X, XS), cons(Y, YS)) -> c_9(quot^#(X, Y), zWquot^#(XS, YS)) } Weak Trs: { minus(X, 0()) -> 0() , minus(s(X), s(Y)) -> minus(X, Y) } Obligation: innermost runtime complexity Answer: MAYBE Due to missing edges in the dependency-graph, the right-hand sides of following rules could be simplified: { zWquot^#(cons(X, XS), cons(Y, YS)) -> c_9(quot^#(X, Y), zWquot^#(XS, YS)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(from^#(s(X))) , sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) , minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y)) , zWquot^#(cons(X, XS), cons(Y, YS)) -> c_4(zWquot^#(XS, YS)) } Weak Trs: { minus(X, 0()) -> 0() , minus(s(X), s(Y)) -> minus(X, Y) } Obligation: innermost runtime complexity Answer: MAYBE No rule is usable, rules are removed from the input problem. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(from^#(s(X))) , sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) , minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y)) , zWquot^#(cons(X, XS), cons(Y, YS)) -> c_4(zWquot^#(XS, YS)) } Obligation: innermost runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: We use the processor 'matrix interpretation of dimension 1' to orient following rules strictly. DPs: { 4: zWquot^#(cons(X, XS), cons(Y, YS)) -> c_4(zWquot^#(XS, YS)) } Sub-proof: ---------- The following argument positions are usable: Uargs(c_1) = {1}, Uargs(c_2) = {1}, Uargs(c_3) = {1}, Uargs(c_4) = {1} TcT has computed the following constructor-based matrix interpretation satisfying not(EDA). [from](x1) = [7] x1 + [0] [cons](x1, x2) = [1] x1 + [1] x2 + [2] [s](x1) = [0] [sel](x1, x2) = [7] x1 + [7] x2 + [0] [0] = [0] [minus](x1, x2) = [7] x1 + [7] x2 + [0] [quot](x1, x2) = [7] x1 + [7] x2 + [0] [zWquot](x1, x2) = [7] x1 + [7] x2 + [0] [nil] = [0] [from^#](x1) = [0] [c_1](x1) = [7] x1 + [0] [sel^#](x1, x2) = [0] [c_2](x1) = [7] x1 + [0] [c_3] = [0] [minus^#](x1, x2) = [0] [c_4] = [0] [c_5](x1) = [7] x1 + [0] [quot^#](x1, x2) = [7] x1 + [7] x2 + [0] [c_6](x1) = [7] x1 + [0] [c_7] = [0] [zWquot^#](x1, x2) = [4] x1 + [1] [c_8] = [0] [c_9](x1, x2) = [7] x1 + [7] x2 + [0] [c_10] = [0] [c] = [0] [c_1](x1) = [1] x1 + [0] [c_2](x1) = [2] x1 + [0] [c_3](x1) = [1] x1 + [0] [c_4](x1) = [1] x1 + [1] The following symbols are considered usable {from^#, sel^#, minus^#, zWquot^#} The order satisfies the following ordering constraints: [from^#(X)] = [0] >= [0] = [c_1(from^#(s(X)))] [sel^#(s(N), cons(X, XS))] = [0] >= [0] = [c_2(sel^#(N, XS))] [minus^#(s(X), s(Y))] = [0] >= [0] = [c_3(minus^#(X, Y))] [zWquot^#(cons(X, XS), cons(Y, YS))] = [4] X + [4] XS + [9] > [4] XS + [2] = [c_4(zWquot^#(XS, YS))] The strictly oriented rules are moved into the weak component. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(from^#(s(X))) , sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) , minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y)) } Weak DPs: { zWquot^#(cons(X, XS), cons(Y, YS)) -> c_4(zWquot^#(XS, YS)) } Obligation: innermost runtime complexity Answer: MAYBE The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. { zWquot^#(cons(X, XS), cons(Y, YS)) -> c_4(zWquot^#(XS, YS)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(from^#(s(X))) , sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) , minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y)) } Obligation: innermost runtime complexity Answer: MAYBE We use the processor 'matrix interpretation of dimension 1' to orient following rules strictly. DPs: { 2: sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) } Sub-proof: ---------- The following argument positions are usable: Uargs(c_1) = {1}, Uargs(c_2) = {1}, Uargs(c_3) = {1} TcT has computed the following constructor-based matrix interpretation satisfying not(EDA). [from](x1) = [7] x1 + [0] [cons](x1, x2) = [1] x1 + [1] x2 + [2] [s](x1) = [0] [sel](x1, x2) = [7] x1 + [7] x2 + [0] [0] = [0] [minus](x1, x2) = [7] x1 + [7] x2 + [0] [quot](x1, x2) = [7] x1 + [7] x2 + [0] [zWquot](x1, x2) = [7] x1 + [7] x2 + [0] [nil] = [0] [from^#](x1) = [0] [c_1](x1) = [7] x1 + [0] [sel^#](x1, x2) = [4] x2 + [1] [c_2](x1) = [7] x1 + [0] [c_3] = [0] [minus^#](x1, x2) = [0] [c_4] = [0] [c_5](x1) = [7] x1 + [0] [quot^#](x1, x2) = [7] x1 + [7] x2 + [0] [c_6](x1) = [7] x1 + [0] [c_7] = [0] [zWquot^#](x1, x2) = [7] x1 + [7] x2 + [0] [c_8] = [0] [c_9](x1, x2) = [7] x1 + [7] x2 + [0] [c_10] = [0] [c] = [0] [c_1](x1) = [1] x1 + [0] [c_2](x1) = [1] x1 + [1] [c_3](x1) = [4] x1 + [0] [c_4](x1) = [7] x1 + [0] The following symbols are considered usable {from^#, sel^#, minus^#} The order satisfies the following ordering constraints: [from^#(X)] = [0] >= [0] = [c_1(from^#(s(X)))] [sel^#(s(N), cons(X, XS))] = [4] X + [4] XS + [9] > [4] XS + [2] = [c_2(sel^#(N, XS))] [minus^#(s(X), s(Y))] = [0] >= [0] = [c_3(minus^#(X, Y))] The strictly oriented rules are moved into the weak component. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(from^#(s(X))) , minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y)) } Weak DPs: { sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) } Obligation: innermost runtime complexity Answer: MAYBE The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. { sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(from^#(s(X))) , minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y)) } Obligation: innermost runtime complexity Answer: MAYBE We use the processor 'matrix interpretation of dimension 1' to orient following rules strictly. DPs: { 2: minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y)) } Sub-proof: ---------- The following argument positions are usable: Uargs(c_1) = {1}, Uargs(c_3) = {1} TcT has computed the following constructor-based matrix interpretation satisfying not(EDA). [from](x1) = [7] x1 + [0] [cons](x1, x2) = [1] x1 + [1] x2 + [0] [s](x1) = [1] x1 + [4] [sel](x1, x2) = [7] x1 + [7] x2 + [0] [0] = [0] [minus](x1, x2) = [7] x1 + [7] x2 + [0] [quot](x1, x2) = [7] x1 + [7] x2 + [0] [zWquot](x1, x2) = [7] x1 + [7] x2 + [0] [nil] = [0] [from^#](x1) = [0] [c_1](x1) = [7] x1 + [0] [sel^#](x1, x2) = [7] x1 + [7] x2 + [0] [c_2](x1) = [7] x1 + [0] [c_3] = [0] [minus^#](x1, x2) = [2] x1 + [1] [c_4] = [0] [c_5](x1) = [7] x1 + [0] [quot^#](x1, x2) = [7] x1 + [7] x2 + [0] [c_6](x1) = [7] x1 + [0] [c_7] = [0] [zWquot^#](x1, x2) = [7] x1 + [7] x2 + [0] [c_8] = [0] [c_9](x1, x2) = [7] x1 + [7] x2 + [0] [c_10] = [0] [c] = [0] [c_1](x1) = [1] x1 + [0] [c_2](x1) = [7] x1 + [0] [c_3](x1) = [1] x1 + [5] [c_4](x1) = [7] x1 + [0] The following symbols are considered usable {from^#, minus^#} The order satisfies the following ordering constraints: [from^#(X)] = [0] >= [0] = [c_1(from^#(s(X)))] [minus^#(s(X), s(Y))] = [2] X + [9] > [2] X + [6] = [c_3(minus^#(X, Y))] The strictly oriented rules are moved into the weak component. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(from^#(s(X))) } Weak DPs: { minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y)) } Obligation: innermost runtime complexity Answer: MAYBE The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. { minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(from^#(s(X))) } Obligation: innermost runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Fastest' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Polynomial Path Order (PS)' failed due to the following reason: The input cannot be shown compatible 2) 'Fastest (timeout of 5 seconds)' failed due to the following reason: Computation stopped due to timeout after 5.0 seconds. 3) 'Polynomial Path Order (PS)' failed due to the following reason: The input cannot be shown compatible Arrrr..