MAYBE 48.09/16.98 MAYBE 48.09/16.98 48.09/16.98 We are left with following problem, upon which TcT provides the 48.09/16.98 certificate MAYBE. 48.09/16.98 48.09/16.98 Strict Trs: 48.09/16.98 { and(true(), X) -> activate(X) 48.09/16.98 , and(false(), Y) -> false() 48.09/16.98 , activate(X) -> X 48.09/16.98 , activate(n__add(X1, X2)) -> add(X1, X2) 48.09/16.98 , activate(n__first(X1, X2)) -> first(X1, X2) 48.09/16.98 , activate(n__from(X)) -> from(X) 48.09/16.98 , activate(n__s(X)) -> s(X) 48.09/16.98 , if(true(), X, Y) -> activate(X) 48.09/16.98 , if(false(), X, Y) -> activate(Y) 48.09/16.98 , add(X1, X2) -> n__add(X1, X2) 48.09/16.98 , add(0(), X) -> activate(X) 48.09/16.98 , add(s(X), Y) -> s(n__add(activate(X), activate(Y))) 48.09/16.98 , s(X) -> n__s(X) 48.09/16.98 , first(X1, X2) -> n__first(X1, X2) 48.09/16.98 , first(0(), X) -> nil() 48.09/16.98 , first(s(X), cons(Y, Z)) -> 48.09/16.98 cons(activate(Y), n__first(activate(X), activate(Z))) 48.09/16.98 , from(X) -> cons(activate(X), n__from(n__s(activate(X)))) 48.09/16.98 , from(X) -> n__from(X) } 48.09/16.98 Obligation: 48.09/16.98 innermost runtime complexity 48.09/16.98 Answer: 48.09/16.98 MAYBE 48.09/16.98 48.09/16.98 Arguments of following rules are not normal-forms: 48.09/16.98 48.09/16.98 { add(s(X), Y) -> s(n__add(activate(X), activate(Y))) 48.09/16.98 , first(s(X), cons(Y, Z)) -> 48.09/16.98 cons(activate(Y), n__first(activate(X), activate(Z))) } 48.09/16.98 48.09/16.98 All above mentioned rules can be savely removed. 48.09/16.98 48.09/16.98 We are left with following problem, upon which TcT provides the 48.09/16.98 certificate MAYBE. 48.09/16.98 48.09/16.98 Strict Trs: 48.09/16.98 { and(true(), X) -> activate(X) 48.09/16.98 , and(false(), Y) -> false() 48.09/16.98 , activate(X) -> X 48.09/16.98 , activate(n__add(X1, X2)) -> add(X1, X2) 48.09/16.98 , activate(n__first(X1, X2)) -> first(X1, X2) 48.09/16.98 , activate(n__from(X)) -> from(X) 48.09/16.98 , activate(n__s(X)) -> s(X) 48.09/16.98 , if(true(), X, Y) -> activate(X) 48.09/16.98 , if(false(), X, Y) -> activate(Y) 48.09/16.98 , add(X1, X2) -> n__add(X1, X2) 48.09/16.98 , add(0(), X) -> activate(X) 48.09/16.98 , s(X) -> n__s(X) 48.09/16.98 , first(X1, X2) -> n__first(X1, X2) 48.09/16.98 , first(0(), X) -> nil() 48.09/16.98 , from(X) -> cons(activate(X), n__from(n__s(activate(X)))) 48.09/16.98 , from(X) -> n__from(X) } 48.09/16.98 Obligation: 48.09/16.98 innermost runtime complexity 48.09/16.98 Answer: 48.09/16.98 MAYBE 48.09/16.98 48.09/16.98 None of the processors succeeded. 48.09/16.98 48.09/16.98 Details of failed attempt(s): 48.09/16.98 ----------------------------- 48.09/16.98 1) 'empty' failed due to the following reason: 48.09/16.98 48.09/16.98 Empty strict component of the problem is NOT empty. 48.09/16.98 48.09/16.98 2) 'Best' failed due to the following reason: 48.09/16.98 48.09/16.98 None of the processors succeeded. 48.09/16.98 48.09/16.98 Details of failed attempt(s): 48.09/16.98 ----------------------------- 48.09/16.98 1) 'Best' failed due to the following reason: 48.09/16.98 48.09/16.98 None of the processors succeeded. 48.09/16.98 48.09/16.98 Details of failed attempt(s): 48.09/16.98 ----------------------------- 48.09/16.98 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 48.09/16.98 seconds)' failed due to the following reason: 48.09/16.98 48.09/16.98 None of the processors succeeded. 48.09/16.98 48.09/16.98 Details of failed attempt(s): 48.09/16.98 ----------------------------- 48.09/16.98 1) 'empty' failed due to the following reason: 48.09/16.98 48.09/16.98 Empty strict component of the problem is NOT empty. 48.09/16.98 48.09/16.98 2) 'With Problem ...' failed due to the following reason: 48.09/16.98 48.09/16.98 None of the processors succeeded. 48.09/16.98 48.09/16.98 Details of failed attempt(s): 48.09/16.98 ----------------------------- 48.09/16.98 1) 'empty' failed due to the following reason: 48.09/16.98 48.09/16.98 Empty strict component of the problem is NOT empty. 48.09/16.98 48.09/16.98 2) 'Fastest' failed due to the following reason: 48.09/16.98 48.09/16.98 None of the processors succeeded. 48.09/16.98 48.09/16.98 Details of failed attempt(s): 48.09/16.98 ----------------------------- 48.09/16.98 1) 'With Problem ...' failed due to the following reason: 48.09/16.98 48.09/16.98 None of the processors succeeded. 48.09/16.98 48.09/16.98 Details of failed attempt(s): 48.09/16.98 ----------------------------- 48.09/16.98 1) 'empty' failed due to the following reason: 48.09/16.98 48.09/16.98 Empty strict component of the problem is NOT empty. 48.09/16.98 48.09/16.98 2) 'With Problem ...' failed due to the following reason: 48.09/16.98 48.09/16.98 None of the processors succeeded. 48.09/16.98 48.09/16.98 Details of failed attempt(s): 48.09/16.98 ----------------------------- 48.09/16.98 1) 'empty' failed due to the following reason: 48.09/16.98 48.09/16.98 Empty strict component of the problem is NOT empty. 48.09/16.98 48.09/16.98 2) 'With Problem ...' failed due to the following reason: 48.09/16.98 48.09/16.98 None of the processors succeeded. 48.09/16.98 48.09/16.98 Details of failed attempt(s): 48.09/16.98 ----------------------------- 48.09/16.98 1) 'empty' failed due to the following reason: 48.09/16.98 48.09/16.98 Empty strict component of the problem is NOT empty. 48.09/16.98 48.09/16.98 2) 'With Problem ...' failed due to the following reason: 48.09/16.98 48.09/16.98 Empty strict component of the problem is NOT empty. 48.09/16.98 48.09/16.98 48.09/16.98 48.09/16.98 48.09/16.98 2) 'With Problem ...' failed due to the following reason: 48.09/16.98 48.09/16.98 None of the processors succeeded. 48.09/16.98 48.09/16.98 Details of failed attempt(s): 48.09/16.98 ----------------------------- 48.09/16.98 1) 'empty' failed due to the following reason: 48.09/16.98 48.09/16.98 Empty strict component of the problem is NOT empty. 48.09/16.98 48.09/16.98 2) 'With Problem ...' failed due to the following reason: 48.09/16.98 48.09/16.98 Empty strict component of the problem is NOT empty. 48.09/16.98 48.09/16.98 48.09/16.98 48.09/16.98 48.09/16.98 48.09/16.98 2) 'Best' failed due to the following reason: 48.09/16.98 48.09/16.98 None of the processors succeeded. 48.09/16.98 48.09/16.98 Details of failed attempt(s): 48.09/16.98 ----------------------------- 48.09/16.98 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 48.09/16.98 following reason: 48.09/16.98 48.09/16.98 The input cannot be shown compatible 48.09/16.98 48.09/16.98 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 48.09/16.98 to the following reason: 48.09/16.98 48.09/16.98 The input cannot be shown compatible 48.09/16.98 48.09/16.98 48.09/16.98 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 48.09/16.98 failed due to the following reason: 48.09/16.98 48.09/16.98 None of the processors succeeded. 48.09/16.98 48.09/16.98 Details of failed attempt(s): 48.09/16.98 ----------------------------- 48.09/16.98 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 48.09/16.98 failed due to the following reason: 48.09/16.98 48.09/16.98 match-boundness of the problem could not be verified. 48.09/16.98 48.09/16.98 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 48.09/16.98 failed due to the following reason: 48.09/16.98 48.09/16.98 match-boundness of the problem could not be verified. 48.09/16.98 48.09/16.98 48.09/16.98 48.09/16.98 2) 'With Problem ... (timeout of 297 seconds)' failed due to the 48.09/16.98 following reason: 48.09/16.98 48.09/16.98 We add the following weak dependency pairs: 48.09/16.98 48.09/16.98 Strict DPs: 48.09/16.98 { and^#(true(), X) -> c_1(activate^#(X)) 48.09/16.98 , and^#(false(), Y) -> c_2() 48.09/16.98 , activate^#(X) -> c_3() 48.09/16.98 , activate^#(n__add(X1, X2)) -> c_4(add^#(X1, X2)) 48.09/16.98 , activate^#(n__first(X1, X2)) -> c_5(first^#(X1, X2)) 48.09/16.98 , activate^#(n__from(X)) -> c_6(from^#(X)) 48.09/16.98 , activate^#(n__s(X)) -> c_7(s^#(X)) 48.09/16.98 , add^#(X1, X2) -> c_10() 48.09/16.98 , add^#(0(), X) -> c_11(activate^#(X)) 48.09/16.98 , first^#(X1, X2) -> c_13() 48.09/16.98 , first^#(0(), X) -> c_14() 48.09/16.98 , from^#(X) -> c_15(activate^#(X), activate^#(X)) 48.09/16.98 , from^#(X) -> c_16() 48.09/16.98 , s^#(X) -> c_12() 48.09/16.98 , if^#(true(), X, Y) -> c_8(activate^#(X)) 48.09/16.98 , if^#(false(), X, Y) -> c_9(activate^#(Y)) } 48.09/16.98 48.09/16.98 and mark the set of starting terms. 48.09/16.98 48.09/16.98 We are left with following problem, upon which TcT provides the 48.09/16.98 certificate MAYBE. 48.09/16.98 48.09/16.98 Strict DPs: 48.09/16.98 { and^#(true(), X) -> c_1(activate^#(X)) 48.09/16.98 , and^#(false(), Y) -> c_2() 48.09/16.98 , activate^#(X) -> c_3() 48.09/16.98 , activate^#(n__add(X1, X2)) -> c_4(add^#(X1, X2)) 48.09/16.98 , activate^#(n__first(X1, X2)) -> c_5(first^#(X1, X2)) 48.09/16.98 , activate^#(n__from(X)) -> c_6(from^#(X)) 48.09/16.98 , activate^#(n__s(X)) -> c_7(s^#(X)) 48.09/16.98 , add^#(X1, X2) -> c_10() 48.09/16.98 , add^#(0(), X) -> c_11(activate^#(X)) 48.09/16.98 , first^#(X1, X2) -> c_13() 48.09/16.98 , first^#(0(), X) -> c_14() 48.09/16.98 , from^#(X) -> c_15(activate^#(X), activate^#(X)) 48.09/16.98 , from^#(X) -> c_16() 48.09/16.98 , s^#(X) -> c_12() 48.09/16.98 , if^#(true(), X, Y) -> c_8(activate^#(X)) 48.09/16.98 , if^#(false(), X, Y) -> c_9(activate^#(Y)) } 48.09/16.98 Strict Trs: 48.09/16.98 { and(true(), X) -> activate(X) 48.09/16.98 , and(false(), Y) -> false() 48.09/16.98 , activate(X) -> X 48.09/16.98 , activate(n__add(X1, X2)) -> add(X1, X2) 48.09/16.98 , activate(n__first(X1, X2)) -> first(X1, X2) 48.09/16.98 , activate(n__from(X)) -> from(X) 48.09/16.98 , activate(n__s(X)) -> s(X) 48.09/16.98 , if(true(), X, Y) -> activate(X) 48.09/16.98 , if(false(), X, Y) -> activate(Y) 48.09/16.98 , add(X1, X2) -> n__add(X1, X2) 48.09/16.98 , add(0(), X) -> activate(X) 48.09/16.98 , s(X) -> n__s(X) 48.09/16.98 , first(X1, X2) -> n__first(X1, X2) 48.09/16.98 , first(0(), X) -> nil() 48.09/16.98 , from(X) -> cons(activate(X), n__from(n__s(activate(X)))) 48.09/16.98 , from(X) -> n__from(X) } 48.09/16.98 Obligation: 48.09/16.98 innermost runtime complexity 48.09/16.98 Answer: 48.09/16.98 MAYBE 48.09/16.98 48.09/16.98 No rule is usable, rules are removed from the input problem. 48.09/16.98 48.09/16.98 We are left with following problem, upon which TcT provides the 48.09/16.98 certificate MAYBE. 48.09/16.98 48.09/16.98 Strict DPs: 48.09/16.98 { and^#(true(), X) -> c_1(activate^#(X)) 48.09/16.98 , and^#(false(), Y) -> c_2() 48.09/16.98 , activate^#(X) -> c_3() 48.09/16.98 , activate^#(n__add(X1, X2)) -> c_4(add^#(X1, X2)) 48.09/16.98 , activate^#(n__first(X1, X2)) -> c_5(first^#(X1, X2)) 48.09/16.98 , activate^#(n__from(X)) -> c_6(from^#(X)) 48.09/16.98 , activate^#(n__s(X)) -> c_7(s^#(X)) 48.09/16.98 , add^#(X1, X2) -> c_10() 48.09/16.98 , add^#(0(), X) -> c_11(activate^#(X)) 48.09/16.98 , first^#(X1, X2) -> c_13() 48.09/16.98 , first^#(0(), X) -> c_14() 48.09/16.98 , from^#(X) -> c_15(activate^#(X), activate^#(X)) 48.09/16.98 , from^#(X) -> c_16() 48.09/16.98 , s^#(X) -> c_12() 48.09/16.98 , if^#(true(), X, Y) -> c_8(activate^#(X)) 48.09/16.98 , if^#(false(), X, Y) -> c_9(activate^#(Y)) } 48.09/16.98 Obligation: 48.09/16.98 innermost runtime complexity 48.09/16.98 Answer: 48.09/16.98 MAYBE 48.09/16.98 48.09/16.98 The weightgap principle applies (using the following constant 48.09/16.98 growth matrix-interpretation) 48.09/16.98 48.09/16.98 The following argument positions are usable: 48.09/16.98 Uargs(c_1) = {1}, Uargs(c_4) = {1}, Uargs(c_5) = {1}, 48.09/16.98 Uargs(c_6) = {1}, Uargs(c_7) = {1}, Uargs(c_8) = {1}, 48.09/16.98 Uargs(c_9) = {1}, Uargs(c_11) = {1}, Uargs(c_15) = {1, 2} 48.09/16.98 48.09/16.98 TcT has computed the following constructor-restricted matrix 48.09/16.98 interpretation. 48.09/16.98 48.09/16.98 [true] = [1] 48.09/16.98 [1] 48.09/16.98 48.09/16.98 [false] = [2] 48.09/16.98 [1] 48.09/16.98 48.09/16.98 [0] = [2] 48.09/16.98 [2] 48.09/16.98 48.09/16.98 [n__add](x1, x2) = [1 2] x1 + [1 2] x2 + [1] 48.09/16.98 [0 1] [0 1] [2] 48.09/16.98 48.09/16.98 [n__first](x1, x2) = [1 2] x1 + [1 2] x2 + [2] 48.09/16.98 [0 1] [0 1] [1] 48.09/16.98 48.09/16.98 [n__from](x1) = [1 2] x1 + [2] 48.09/16.98 [0 1] [1] 48.09/16.98 48.09/16.98 [n__s](x1) = [1 2] x1 + [1] 48.09/16.98 [0 1] [2] 48.09/16.98 48.09/16.98 [and^#](x1, x2) = [2 2] x1 + [2 2] x2 + [1] 48.09/16.98 [1 2] [1 2] [1] 48.09/16.98 48.09/16.98 [c_1](x1) = [1 0] x1 + [1] 48.09/16.98 [0 1] [1] 48.09/16.98 48.09/16.98 [activate^#](x1) = [0 0] x1 + [2] 48.09/16.98 [1 1] [1] 48.09/16.98 48.09/16.98 [c_2] = [2] 48.09/16.98 [1] 48.09/16.98 48.09/16.98 [c_3] = [1] 48.09/16.98 [1] 48.09/16.98 48.09/16.98 [c_4](x1) = [1 0] x1 + [2] 48.09/16.98 [0 1] [1] 48.09/16.98 48.09/16.98 [add^#](x1, x2) = [0 0] x1 + [0 0] x2 + [1] 48.09/16.98 [1 0] [2 1] [2] 48.09/16.98 48.09/16.98 [c_5](x1) = [1 0] x1 + [2] 48.09/16.98 [0 1] [1] 48.09/16.98 48.09/16.98 [first^#](x1, x2) = [0 0] x1 + [0 0] x2 + [1] 48.09/16.98 [2 1] [1 1] [1] 48.09/16.98 48.09/16.98 [c_6](x1) = [1 0] x1 + [2] 48.09/16.98 [0 1] [2] 48.09/16.98 48.09/16.98 [from^#](x1) = [0 0] x1 + [1] 48.09/16.98 [1 1] [1] 48.09/16.98 48.09/16.98 [c_7](x1) = [1 0] x1 + [2] 48.09/16.98 [0 1] [2] 48.09/16.98 48.09/16.98 [s^#](x1) = [0 0] x1 + [1] 48.09/16.98 [1 1] [1] 48.09/16.98 48.09/16.98 [if^#](x1, x2, x3) = [1 2] x1 + [1 1] x2 + [1 2] x3 + [1] 48.09/16.98 [2 2] [1 2] [2 1] [1] 48.09/16.98 48.09/16.98 [c_8](x1) = [1 0] x1 + [1] 48.09/16.98 [0 1] [1] 48.09/16.98 48.09/16.98 [c_9](x1) = [1 0] x1 + [1] 48.09/16.98 [0 1] [1] 48.09/16.98 48.09/16.98 [c_10] = [0] 48.09/16.98 [2] 48.09/16.98 48.09/16.98 [c_11](x1) = [1 0] x1 + [1] 48.09/16.98 [0 1] [1] 48.09/16.98 48.09/16.98 [c_12] = [0] 48.09/16.98 [1] 48.09/16.98 48.09/16.98 [c_13] = [0] 48.09/16.98 [1] 48.09/16.98 48.09/16.98 [c_14] = [0] 48.09/16.98 [2] 48.09/16.98 48.09/16.98 [c_15](x1, x2) = [1 0] x1 + [1 0] x2 + [2] 48.09/16.98 [0 1] [0 1] [1] 48.09/16.98 48.09/16.98 [c_16] = [0] 48.09/16.98 [1] 48.09/16.98 48.09/16.98 The order satisfies the following ordering constraints: 48.09/16.98 48.09/16.98 [and^#(true(), X)] = [2 2] X + [5] 48.09/16.98 [1 2] [4] 48.09/16.98 > [0 0] X + [3] 48.09/16.98 [1 1] [2] 48.09/16.98 = [c_1(activate^#(X))] 48.09/16.98 48.09/16.98 [and^#(false(), Y)] = [2 2] Y + [7] 48.09/16.98 [1 2] [5] 48.09/16.98 > [2] 48.09/16.98 [1] 48.09/16.98 = [c_2()] 48.09/16.98 48.09/16.98 [activate^#(X)] = [0 0] X + [2] 48.09/16.98 [1 1] [1] 48.09/16.98 > [1] 48.09/16.98 [1] 48.09/16.98 = [c_3()] 48.09/16.98 48.09/16.98 [activate^#(n__add(X1, X2))] = [0 0] X1 + [0 0] X2 + [2] 48.09/16.98 [1 3] [1 3] [4] 48.09/16.98 ? [0 0] X1 + [0 0] X2 + [3] 48.09/16.98 [1 0] [2 1] [3] 48.09/16.98 = [c_4(add^#(X1, X2))] 48.09/16.98 48.09/16.98 [activate^#(n__first(X1, X2))] = [0 0] X1 + [0 0] X2 + [2] 48.09/16.98 [1 3] [1 3] [4] 48.09/16.98 ? [0 0] X1 + [0 0] X2 + [3] 48.09/16.98 [2 1] [1 1] [2] 48.09/16.98 = [c_5(first^#(X1, X2))] 48.09/16.98 48.09/16.98 [activate^#(n__from(X))] = [0 0] X + [2] 48.09/16.98 [1 3] [4] 48.09/16.98 ? [0 0] X + [3] 48.09/16.98 [1 1] [3] 48.09/16.98 = [c_6(from^#(X))] 48.09/16.98 48.09/16.98 [activate^#(n__s(X))] = [0 0] X + [2] 48.09/16.98 [1 3] [4] 48.09/16.98 ? [0 0] X + [3] 48.09/16.98 [1 1] [3] 48.09/16.98 = [c_7(s^#(X))] 48.09/16.98 48.09/16.98 [add^#(X1, X2)] = [0 0] X1 + [0 0] X2 + [1] 48.09/16.98 [1 0] [2 1] [2] 48.09/16.98 > [0] 48.09/16.98 [2] 48.09/16.98 = [c_10()] 48.09/16.98 48.09/16.98 [add^#(0(), X)] = [0 0] X + [1] 48.09/16.98 [2 1] [4] 48.09/16.98 ? [0 0] X + [3] 48.09/16.98 [1 1] [2] 48.09/16.98 = [c_11(activate^#(X))] 48.09/16.98 48.09/16.98 [first^#(X1, X2)] = [0 0] X1 + [0 0] X2 + [1] 48.09/16.98 [2 1] [1 1] [1] 48.09/16.98 > [0] 48.09/16.98 [1] 48.09/16.98 = [c_13()] 48.09/16.98 48.09/16.98 [first^#(0(), X)] = [0 0] X + [1] 48.09/16.98 [1 1] [7] 48.09/16.98 > [0] 48.09/16.98 [2] 48.09/16.98 = [c_14()] 48.09/16.98 48.09/16.98 [from^#(X)] = [0 0] X + [1] 48.09/16.98 [1 1] [1] 48.09/16.98 ? [0 0] X + [6] 48.09/16.98 [2 2] [3] 48.09/16.98 = [c_15(activate^#(X), activate^#(X))] 48.09/16.98 48.09/16.98 [from^#(X)] = [0 0] X + [1] 48.09/16.98 [1 1] [1] 48.09/16.98 > [0] 48.09/16.98 [1] 48.09/16.98 = [c_16()] 48.09/16.98 48.09/16.98 [s^#(X)] = [0 0] X + [1] 48.09/16.98 [1 1] [1] 48.09/16.98 > [0] 48.09/16.98 [1] 48.09/16.98 = [c_12()] 48.09/16.98 48.09/16.98 [if^#(true(), X, Y)] = [1 1] X + [1 2] Y + [4] 48.09/16.98 [1 2] [2 1] [5] 48.09/16.98 > [0 0] X + [3] 48.09/16.98 [1 1] [2] 48.09/16.98 = [c_8(activate^#(X))] 48.09/16.98 48.09/16.98 [if^#(false(), X, Y)] = [1 1] X + [1 2] Y + [5] 48.09/16.98 [1 2] [2 1] [7] 48.09/16.98 > [0 0] Y + [3] 48.09/16.98 [1 1] [2] 48.09/16.98 = [c_9(activate^#(Y))] 48.09/16.99 48.09/16.99 48.09/16.99 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 48.09/16.99 48.09/16.99 We are left with following problem, upon which TcT provides the 48.09/16.99 certificate MAYBE. 48.09/16.99 48.09/16.99 Strict DPs: 48.09/16.99 { activate^#(n__add(X1, X2)) -> c_4(add^#(X1, X2)) 48.09/16.99 , activate^#(n__first(X1, X2)) -> c_5(first^#(X1, X2)) 48.09/16.99 , activate^#(n__from(X)) -> c_6(from^#(X)) 48.09/16.99 , activate^#(n__s(X)) -> c_7(s^#(X)) 48.09/16.99 , add^#(0(), X) -> c_11(activate^#(X)) 48.09/16.99 , from^#(X) -> c_15(activate^#(X), activate^#(X)) } 48.09/16.99 Weak DPs: 48.09/16.99 { and^#(true(), X) -> c_1(activate^#(X)) 48.09/16.99 , and^#(false(), Y) -> c_2() 48.09/16.99 , activate^#(X) -> c_3() 48.09/16.99 , add^#(X1, X2) -> c_10() 48.09/16.99 , first^#(X1, X2) -> c_13() 48.09/16.99 , first^#(0(), X) -> c_14() 48.09/16.99 , from^#(X) -> c_16() 48.09/16.99 , s^#(X) -> c_12() 48.09/16.99 , if^#(true(), X, Y) -> c_8(activate^#(X)) 48.09/16.99 , if^#(false(), X, Y) -> c_9(activate^#(Y)) } 48.09/16.99 Obligation: 48.09/16.99 innermost runtime complexity 48.09/16.99 Answer: 48.09/16.99 MAYBE 48.09/16.99 48.09/16.99 The following weak DPs constitute a sub-graph of the DG that is 48.09/16.99 closed under successors. The DPs are removed. 48.09/16.99 48.09/16.99 { and^#(false(), Y) -> c_2() 48.09/16.99 , activate^#(X) -> c_3() 48.09/16.99 , add^#(X1, X2) -> c_10() 48.09/16.99 , first^#(X1, X2) -> c_13() 48.09/16.99 , first^#(0(), X) -> c_14() 48.09/16.99 , from^#(X) -> c_16() 48.09/16.99 , s^#(X) -> c_12() } 48.09/16.99 48.09/16.99 We are left with following problem, upon which TcT provides the 48.09/16.99 certificate MAYBE. 48.09/16.99 48.09/16.99 Strict DPs: 48.09/16.99 { activate^#(n__add(X1, X2)) -> c_4(add^#(X1, X2)) 48.09/16.99 , activate^#(n__first(X1, X2)) -> c_5(first^#(X1, X2)) 48.09/16.99 , activate^#(n__from(X)) -> c_6(from^#(X)) 48.09/16.99 , activate^#(n__s(X)) -> c_7(s^#(X)) 48.09/16.99 , add^#(0(), X) -> c_11(activate^#(X)) 48.09/16.99 , from^#(X) -> c_15(activate^#(X), activate^#(X)) } 48.09/16.99 Weak DPs: 48.09/16.99 { and^#(true(), X) -> c_1(activate^#(X)) 48.09/16.99 , if^#(true(), X, Y) -> c_8(activate^#(X)) 48.09/16.99 , if^#(false(), X, Y) -> c_9(activate^#(Y)) } 48.09/16.99 Obligation: 48.09/16.99 innermost runtime complexity 48.09/16.99 Answer: 48.09/16.99 MAYBE 48.09/16.99 48.09/16.99 Due to missing edges in the dependency-graph, the right-hand sides 48.09/16.99 of following rules could be simplified: 48.09/16.99 48.09/16.99 { activate^#(n__first(X1, X2)) -> c_5(first^#(X1, X2)) 48.09/16.99 , activate^#(n__s(X)) -> c_7(s^#(X)) } 48.09/16.99 48.09/16.99 We are left with following problem, upon which TcT provides the 48.09/16.99 certificate MAYBE. 48.09/16.99 48.09/16.99 Strict DPs: 48.09/16.99 { activate^#(n__add(X1, X2)) -> c_1(add^#(X1, X2)) 48.09/16.99 , activate^#(n__first(X1, X2)) -> c_2() 48.09/16.99 , activate^#(n__from(X)) -> c_3(from^#(X)) 48.09/16.99 , activate^#(n__s(X)) -> c_4() 48.09/16.99 , add^#(0(), X) -> c_5(activate^#(X)) 48.09/16.99 , from^#(X) -> c_6(activate^#(X), activate^#(X)) } 48.09/16.99 Weak DPs: 48.09/16.99 { and^#(true(), X) -> c_7(activate^#(X)) 48.09/16.99 , if^#(true(), X, Y) -> c_8(activate^#(X)) 48.09/16.99 , if^#(false(), X, Y) -> c_9(activate^#(Y)) } 48.09/16.99 Obligation: 48.09/16.99 innermost runtime complexity 48.09/16.99 Answer: 48.09/16.99 MAYBE 48.09/16.99 48.09/16.99 Consider the dependency graph 48.09/16.99 48.09/16.99 1: activate^#(n__add(X1, X2)) -> c_1(add^#(X1, X2)) 48.09/16.99 -->_1 add^#(0(), X) -> c_5(activate^#(X)) :5 48.09/16.99 48.09/16.99 2: activate^#(n__first(X1, X2)) -> c_2() 48.09/16.99 48.09/16.99 3: activate^#(n__from(X)) -> c_3(from^#(X)) 48.09/16.99 -->_1 from^#(X) -> c_6(activate^#(X), activate^#(X)) :6 48.09/16.99 48.09/16.99 4: activate^#(n__s(X)) -> c_4() 48.09/16.99 48.09/16.99 5: add^#(0(), X) -> c_5(activate^#(X)) 48.09/16.99 -->_1 activate^#(n__s(X)) -> c_4() :4 48.09/16.99 -->_1 activate^#(n__from(X)) -> c_3(from^#(X)) :3 48.09/16.99 -->_1 activate^#(n__first(X1, X2)) -> c_2() :2 48.09/16.99 -->_1 activate^#(n__add(X1, X2)) -> c_1(add^#(X1, X2)) :1 48.09/16.99 48.09/16.99 6: from^#(X) -> c_6(activate^#(X), activate^#(X)) 48.09/16.99 -->_2 activate^#(n__s(X)) -> c_4() :4 48.09/16.99 -->_1 activate^#(n__s(X)) -> c_4() :4 48.09/16.99 -->_2 activate^#(n__from(X)) -> c_3(from^#(X)) :3 48.09/16.99 -->_1 activate^#(n__from(X)) -> c_3(from^#(X)) :3 48.09/16.99 -->_2 activate^#(n__first(X1, X2)) -> c_2() :2 48.09/16.99 -->_1 activate^#(n__first(X1, X2)) -> c_2() :2 48.09/16.99 -->_2 activate^#(n__add(X1, X2)) -> c_1(add^#(X1, X2)) :1 48.09/16.99 -->_1 activate^#(n__add(X1, X2)) -> c_1(add^#(X1, X2)) :1 48.09/16.99 48.09/16.99 7: and^#(true(), X) -> c_7(activate^#(X)) 48.09/16.99 -->_1 activate^#(n__s(X)) -> c_4() :4 48.09/16.99 -->_1 activate^#(n__from(X)) -> c_3(from^#(X)) :3 48.09/16.99 -->_1 activate^#(n__first(X1, X2)) -> c_2() :2 48.09/16.99 -->_1 activate^#(n__add(X1, X2)) -> c_1(add^#(X1, X2)) :1 48.09/16.99 48.09/16.99 8: if^#(true(), X, Y) -> c_8(activate^#(X)) 48.09/16.99 -->_1 activate^#(n__s(X)) -> c_4() :4 48.09/16.99 -->_1 activate^#(n__from(X)) -> c_3(from^#(X)) :3 48.09/16.99 -->_1 activate^#(n__first(X1, X2)) -> c_2() :2 48.09/16.99 -->_1 activate^#(n__add(X1, X2)) -> c_1(add^#(X1, X2)) :1 48.09/16.99 48.09/16.99 9: if^#(false(), X, Y) -> c_9(activate^#(Y)) 48.09/16.99 -->_1 activate^#(n__s(X)) -> c_4() :4 48.09/16.99 -->_1 activate^#(n__from(X)) -> c_3(from^#(X)) :3 48.09/16.99 -->_1 activate^#(n__first(X1, X2)) -> c_2() :2 48.09/16.99 -->_1 activate^#(n__add(X1, X2)) -> c_1(add^#(X1, X2)) :1 48.09/16.99 48.09/16.99 48.09/16.99 Following roots of the dependency graph are removed, as the 48.09/16.99 considered set of starting terms is closed under reduction with 48.09/16.99 respect to these rules (modulo compound contexts). 48.09/16.99 48.09/16.99 { and^#(true(), X) -> c_7(activate^#(X)) 48.09/16.99 , if^#(true(), X, Y) -> c_8(activate^#(X)) 48.09/16.99 , if^#(false(), X, Y) -> c_9(activate^#(Y)) } 48.09/16.99 48.09/16.99 48.09/16.99 We are left with following problem, upon which TcT provides the 48.09/16.99 certificate MAYBE. 48.09/16.99 48.09/16.99 Strict DPs: 48.09/16.99 { activate^#(n__add(X1, X2)) -> c_1(add^#(X1, X2)) 48.09/16.99 , activate^#(n__first(X1, X2)) -> c_2() 48.09/16.99 , activate^#(n__from(X)) -> c_3(from^#(X)) 48.09/16.99 , activate^#(n__s(X)) -> c_4() 48.09/16.99 , add^#(0(), X) -> c_5(activate^#(X)) 48.09/16.99 , from^#(X) -> c_6(activate^#(X), activate^#(X)) } 48.09/16.99 Obligation: 48.09/16.99 innermost runtime complexity 48.09/16.99 Answer: 48.09/16.99 MAYBE 48.09/16.99 48.09/16.99 We estimate the number of application of {2,4} by applications of 48.09/16.99 Pre({2,4}) = {5,6}. Here rules are labeled as follows: 48.09/16.99 48.09/16.99 DPs: 48.09/16.99 { 1: activate^#(n__add(X1, X2)) -> c_1(add^#(X1, X2)) 48.09/16.99 , 2: activate^#(n__first(X1, X2)) -> c_2() 48.09/16.99 , 3: activate^#(n__from(X)) -> c_3(from^#(X)) 48.09/16.99 , 4: activate^#(n__s(X)) -> c_4() 48.09/16.99 , 5: add^#(0(), X) -> c_5(activate^#(X)) 48.09/16.99 , 6: from^#(X) -> c_6(activate^#(X), activate^#(X)) } 48.09/16.99 48.09/16.99 We are left with following problem, upon which TcT provides the 48.09/16.99 certificate MAYBE. 48.09/16.99 48.09/16.99 Strict DPs: 48.09/16.99 { activate^#(n__add(X1, X2)) -> c_1(add^#(X1, X2)) 48.09/16.99 , activate^#(n__from(X)) -> c_3(from^#(X)) 48.09/16.99 , add^#(0(), X) -> c_5(activate^#(X)) 48.09/16.99 , from^#(X) -> c_6(activate^#(X), activate^#(X)) } 48.09/16.99 Weak DPs: 48.09/16.99 { activate^#(n__first(X1, X2)) -> c_2() 48.09/16.99 , activate^#(n__s(X)) -> c_4() } 48.09/16.99 Obligation: 48.09/16.99 innermost runtime complexity 48.09/16.99 Answer: 48.09/16.99 MAYBE 48.09/16.99 48.09/16.99 The following weak DPs constitute a sub-graph of the DG that is 48.09/16.99 closed under successors. The DPs are removed. 48.09/16.99 48.09/16.99 { activate^#(n__first(X1, X2)) -> c_2() 48.09/16.99 , activate^#(n__s(X)) -> c_4() } 48.09/16.99 48.09/16.99 We are left with following problem, upon which TcT provides the 48.09/16.99 certificate MAYBE. 48.09/16.99 48.09/16.99 Strict DPs: 48.09/16.99 { activate^#(n__add(X1, X2)) -> c_1(add^#(X1, X2)) 48.09/16.99 , activate^#(n__from(X)) -> c_3(from^#(X)) 48.09/16.99 , add^#(0(), X) -> c_5(activate^#(X)) 48.09/16.99 , from^#(X) -> c_6(activate^#(X), activate^#(X)) } 48.09/16.99 Obligation: 48.09/16.99 innermost runtime complexity 48.09/16.99 Answer: 48.09/16.99 MAYBE 48.09/16.99 48.09/16.99 None of the processors succeeded. 48.09/16.99 48.09/16.99 Details of failed attempt(s): 48.09/16.99 ----------------------------- 48.09/16.99 1) 'empty' failed due to the following reason: 48.09/16.99 48.09/16.99 Empty strict component of the problem is NOT empty. 48.09/16.99 48.09/16.99 2) 'With Problem ...' failed due to the following reason: 48.09/16.99 48.09/16.99 None of the processors succeeded. 48.09/16.99 48.09/16.99 Details of failed attempt(s): 48.09/16.99 ----------------------------- 48.09/16.99 1) 'empty' failed due to the following reason: 48.09/16.99 48.09/16.99 Empty strict component of the problem is NOT empty. 48.09/16.99 48.09/16.99 2) 'Fastest' failed due to the following reason: 48.09/16.99 48.09/16.99 None of the processors succeeded. 48.09/16.99 48.09/16.99 Details of failed attempt(s): 48.09/16.99 ----------------------------- 48.09/16.99 1) 'With Problem ...' failed due to the following reason: 48.09/16.99 48.09/16.99 None of the processors succeeded. 48.09/16.99 48.09/16.99 Details of failed attempt(s): 48.09/16.99 ----------------------------- 48.09/16.99 1) 'empty' failed due to the following reason: 48.09/16.99 48.09/16.99 Empty strict component of the problem is NOT empty. 48.09/16.99 48.09/16.99 2) 'Polynomial Path Order (PS)' failed due to the following reason: 48.09/16.99 48.09/16.99 The input cannot be shown compatible 48.09/16.99 48.09/16.99 48.09/16.99 2) 'Polynomial Path Order (PS)' failed due to the following reason: 48.09/16.99 48.09/16.99 The input cannot be shown compatible 48.09/16.99 48.09/16.99 3) 'Fastest (timeout of 24 seconds)' failed due to the following 48.09/16.99 reason: 48.09/16.99 48.09/16.99 None of the processors succeeded. 48.09/16.99 48.09/16.99 Details of failed attempt(s): 48.09/16.99 ----------------------------- 48.09/16.99 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 48.09/16.99 failed due to the following reason: 48.09/16.99 48.09/16.99 match-boundness of the problem could not be verified. 48.09/16.99 48.09/16.99 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 48.09/16.99 failed due to the following reason: 48.09/16.99 48.09/16.99 match-boundness of the problem could not be verified. 48.09/16.99 48.09/16.99 48.09/16.99 48.09/16.99 48.09/16.99 48.09/16.99 48.09/16.99 48.09/16.99 Arrrr.. 48.37/17.01 EOF