- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] active(from(X)) -> mark(cons(X,from(s(X)))) [2] active(length(nil)) -> mark(0) [3] active(length(cons(X,Y))) -> mark(s(length1(Y))) [4] active(length1(X)) -> mark(length(X)) [5] active(from(X)) -> from(active(X)) [6] active(cons(X1,X2)) -> cons(active(X1),X2) [7] active(s(X)) -> s(active(X)) [8] from(mark(X)) -> mark(from(X)) [9] cons(mark(X1),X2) -> mark(cons(X1,X2)) [10] s(mark(X)) -> mark(s(X)) [11] proper(from(X)) -> from(proper(X)) [12] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) [13] proper(s(X)) -> s(proper(X)) [14] proper(length(X)) -> length(proper(X)) [15] proper(nil) -> ok(nil) [16] proper(0) -> ok(0) [17] proper(length1(X)) -> length1(proper(X)) [18] from(ok(X)) -> ok(from(X)) [19] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) [20] s(ok(X)) -> ok(s(X)) [21] length(ok(X)) -> ok(length(X)) [22] length1(ok(X)) -> ok(length1(X)) [23] top(mark(X)) -> top(proper(X)) [24] top(ok(X)) -> top(active(X)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 8 components: { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> } { --> } { --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { cons(mark(X1),X2) >= mark(cons(X1,X2)) ; cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ; from(mark(X)) >= mark(from(X)) ; from(ok(X)) >= ok(from(X)) ; s(mark(X)) >= mark(s(X)) ; s(ok(X)) >= ok(s(X)) ; active(cons(X1,X2)) >= cons(active(X1),X2) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; active(from(X)) >= from(active(X)) ; active(s(X)) >= s(active(X)) ; active(length(cons(X,Y))) >= mark(s(length1(Y))) ; active(length(nil)) >= mark(0) ; active(length1(X)) >= mark(length(X)) ; length(ok(X)) >= ok(length(X)) ; length1(ok(X)) >= ok(length1(X)) ; proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ; proper(from(X)) >= from(proper(X)) ; proper(s(X)) >= s(proper(X)) ; proper(0) >= ok(0) ; proper(length(X)) >= length(proper(X)) ; proper(nil) >= ok(nil) ; proper(length1(X)) >= length1(proper(X)) ; top(mark(X)) >= top(proper(X)) ; top(ok(X)) >= top(active(X)) ; Marked_top(mark(X)) >= Marked_top(proper(X)) ; Marked_top(ok(X)) >= Marked_top(active(X)) ; } + Disjunctions:{ { Marked_top(mark(X)) > Marked_top(proper(X)) ; } { Marked_top(ok(X)) > Marked_top(active(X)) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. === TIMER virtual : 50.000000 === trying sub matrices of size: 1 Matrix interpretation constraints generated. Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. Termination constraints generated. Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 50.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: cons(mark(X1),X2) >= mark(cons(X1,X2)) constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) constraint: from(mark(X)) >= mark(from(X)) constraint: from(ok(X)) >= ok(from(X)) constraint: s(mark(X)) >= mark(s(X)) constraint: s(ok(X)) >= ok(s(X)) constraint: active(cons(X1,X2)) >= cons(active(X1),X2) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: active(from(X)) >= from(active(X)) constraint: active(s(X)) >= s(active(X)) constraint: active(length(cons(X,Y))) >= mark(s(length1(Y))) constraint: active(length(nil)) >= mark(0) constraint: active(length1(X)) >= mark(length(X)) constraint: length(ok(X)) >= ok(length(X)) constraint: length1(ok(X)) >= ok(length1(X)) constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) constraint: proper(from(X)) >= from(proper(X)) constraint: proper(s(X)) >= s(proper(X)) constraint: proper(0) >= ok(0) constraint: proper(length(X)) >= length(proper(X)) constraint: proper(nil) >= ok(nil) constraint: proper(length1(X)) >= length1(proper(X)) constraint: top(mark(X)) >= top(proper(X)) constraint: top(ok(X)) >= top(active(X)) constraint: Marked_top(mark(X)) >= Marked_top(proper(X)) constraint: Marked_top(ok(X)) >= Marked_top(active(X)) APPLY CRITERIA (Subterm criterion) ST: Marked_proper -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_active -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_length1 -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_length -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_from -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_cons -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_s -> 1 APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { cons(mark(X1),X2) >= mark(cons(X1,X2)) ; cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ; from(mark(X)) >= mark(from(X)) ; from(ok(X)) >= ok(from(X)) ; s(mark(X)) >= mark(s(X)) ; s(ok(X)) >= ok(s(X)) ; active(cons(X1,X2)) >= cons(active(X1),X2) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; active(from(X)) >= from(active(X)) ; active(s(X)) >= s(active(X)) ; active(length(cons(X,Y))) >= mark(s(length1(Y))) ; active(length(nil)) >= mark(0) ; active(length1(X)) >= mark(length(X)) ; length(ok(X)) >= ok(length(X)) ; length1(ok(X)) >= ok(length1(X)) ; proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ; proper(from(X)) >= from(proper(X)) ; proper(s(X)) >= s(proper(X)) ; proper(0) >= ok(0) ; proper(length(X)) >= length(proper(X)) ; proper(nil) >= ok(nil) ; proper(length1(X)) >= length1(proper(X)) ; top(mark(X)) >= top(proper(X)) ; top(ok(X)) >= top(active(X)) ; Marked_top(ok(X)) >= Marked_top(active(X)) ; } + Disjunctions:{ { Marked_top(ok(X)) > Marked_top(active(X)) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: cons(mark(X1),X2) >= mark(cons(X1,X2)) constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) constraint: from(mark(X)) >= mark(from(X)) constraint: from(ok(X)) >= ok(from(X)) constraint: s(mark(X)) >= mark(s(X)) constraint: s(ok(X)) >= ok(s(X)) constraint: active(cons(X1,X2)) >= cons(active(X1),X2) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: active(from(X)) >= from(active(X)) constraint: active(s(X)) >= s(active(X)) constraint: active(length(cons(X,Y))) >= mark(s(length1(Y))) constraint: active(length(nil)) >= mark(0) constraint: active(length1(X)) >= mark(length(X)) constraint: length(ok(X)) >= ok(length(X)) constraint: length1(ok(X)) >= ok(length1(X)) constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) constraint: proper(from(X)) >= from(proper(X)) constraint: proper(s(X)) >= s(proper(X)) constraint: proper(0) >= ok(0) constraint: proper(length(X)) >= length(proper(X)) constraint: proper(nil) >= ok(nil) constraint: proper(length1(X)) >= length1(proper(X)) constraint: top(mark(X)) >= top(proper(X)) constraint: top(ok(X)) >= top(active(X)) constraint: Marked_top(ok(X)) >= Marked_top(active(X)) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_cons -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] active(from(X)) -> mark(cons(X,from(s(X)))) [2] active(length(nil)) -> mark(0) [3] active(length(cons(X,Y))) -> mark(s(length1(Y))) [4] active(length1(X)) -> mark(length(X)) [5] active(from(X)) -> from(active(X)) [6] active(cons(X1,X2)) -> cons(active(X1),X2) [7] active(s(X)) -> s(active(X)) [8] from(mark(X)) -> mark(from(X)) [9] cons(mark(X1),X2) -> mark(cons(X1,X2)) [10] s(mark(X)) -> mark(s(X)) [11] proper(from(X)) -> from(proper(X)) [12] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) [13] proper(s(X)) -> s(proper(X)) [14] proper(length(X)) -> length(proper(X)) [15] proper(nil) -> ok(nil) [16] proper(0) -> ok(0) [17] proper(length1(X)) -> length1(proper(X)) [18] from(ok(X)) -> ok(from(X)) [19] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) [20] s(ok(X)) -> ok(s(X)) [21] length(ok(X)) -> ok(length(X)) [22] length1(ok(X)) -> ok(length1(X)) [23] top(mark(X)) -> top(proper(X)) [24] top(ok(X)) -> top(active(X)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ mark ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ length1 ] (X0) = [ [ 0 , 1 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ active ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ Marked_top ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ from ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ ok ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ length ] (X0) = [ [ 0 , 1 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ cons ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 1 , 1 ] [ 0 , 1 , 1 ] ]*X1 + [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 1 , 1 , 0 ] [ 1 , 1 , 0 ] ]; [ proper ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 0 , 1 ] [ 0 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ 0 ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ s ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ top ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ nil ] () = [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 1 , 0 , 0 ] ]; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ mark ] (X0) = 0; [ length1 ] (X0) = 1 + 0; [ active ] (X0) = 0; [ Marked_top ] (X0) = 1*X0 + 0; [ from ] (X0) = 2*X0 + 0; [ ok ] (X0) = 1 + 0; [ length ] (X0) = 2 + 0; [ cons ] (X0,X1) = 1*X0 + 0; [ proper ] (X0) = 1*X0 + 0; [ 0 ] () = 1 + 0; [ s ] (X0) = 2*X0 + 0; [ top ] (X0) = 0; [ nil ] () = 1 + 0; ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 3.843000 seconds (real time) Cime Exit Status: 0