- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] active(first(0,X)) -> mark(nil) [2] active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) [3] active(from(X)) -> mark(cons(X,from(s(X)))) [4] active(first(X1,X2)) -> first(active(X1),X2) [5] active(first(X1,X2)) -> first(X1,active(X2)) [6] active(s(X)) -> s(active(X)) [7] active(cons(X1,X2)) -> cons(active(X1),X2) [8] active(from(X)) -> from(active(X)) [9] first(mark(X1),X2) -> mark(first(X1,X2)) [10] first(X1,mark(X2)) -> mark(first(X1,X2)) [11] s(mark(X)) -> mark(s(X)) [12] cons(mark(X1),X2) -> mark(cons(X1,X2)) [13] from(mark(X)) -> mark(from(X)) [14] proper(first(X1,X2)) -> first(proper(X1),proper(X2)) [15] proper(0) -> ok(0) [16] proper(nil) -> ok(nil) [17] proper(s(X)) -> s(proper(X)) [18] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) [19] proper(from(X)) -> from(proper(X)) [20] first(ok(X1),ok(X2)) -> ok(first(X1,X2)) [21] s(ok(X)) -> ok(s(X)) [22] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) [23] from(ok(X)) -> ok(from(X)) [24] top(mark(X)) -> top(proper(X)) [25] top(ok(X)) -> top(active(X)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 7 components: { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { active(first(0,X)) >= mark(nil) ; active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) ; active(first(X1,X2)) >= first(active(X1),X2) ; active(first(X1,X2)) >= first(X1,active(X2)) ; active(cons(X1,X2)) >= cons(active(X1),X2) ; active(s(X)) >= s(active(X)) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; active(from(X)) >= from(active(X)) ; first(mark(X1),X2) >= mark(first(X1,X2)) ; first(ok(X1),ok(X2)) >= ok(first(X1,X2)) ; first(X1,mark(X2)) >= mark(first(X1,X2)) ; cons(mark(X1),X2) >= mark(cons(X1,X2)) ; cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ; s(mark(X)) >= mark(s(X)) ; s(ok(X)) >= ok(s(X)) ; from(mark(X)) >= mark(from(X)) ; from(ok(X)) >= ok(from(X)) ; proper(nil) >= ok(nil) ; proper(first(X1,X2)) >= first(proper(X1),proper(X2)) ; proper(0) >= ok(0) ; proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ; proper(s(X)) >= s(proper(X)) ; proper(from(X)) >= from(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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: active(first(0,X)) >= mark(nil) constraint: active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) constraint: active(first(X1,X2)) >= first(active(X1),X2) constraint: active(first(X1,X2)) >= first(X1,active(X2)) constraint: active(cons(X1,X2)) >= cons(active(X1),X2) constraint: active(s(X)) >= s(active(X)) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: active(from(X)) >= from(active(X)) constraint: first(mark(X1),X2) >= mark(first(X1,X2)) constraint: first(ok(X1),ok(X2)) >= ok(first(X1,X2)) constraint: first(X1,mark(X2)) >= mark(first(X1,X2)) constraint: cons(mark(X1),X2) >= mark(cons(X1,X2)) constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) constraint: s(mark(X)) >= mark(s(X)) constraint: s(ok(X)) >= ok(s(X)) constraint: from(mark(X)) >= mark(from(X)) constraint: from(ok(X)) >= ok(from(X)) constraint: proper(nil) >= ok(nil) constraint: proper(first(X1,X2)) >= first(proper(X1),proper(X2)) constraint: proper(0) >= ok(0) constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) constraint: proper(s(X)) >= s(proper(X)) constraint: proper(from(X)) >= from(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_first -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_s -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_cons -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_from -> 1 APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { active(first(0,X)) >= mark(nil) ; active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) ; active(first(X1,X2)) >= first(active(X1),X2) ; active(first(X1,X2)) >= first(X1,active(X2)) ; active(cons(X1,X2)) >= cons(active(X1),X2) ; active(s(X)) >= s(active(X)) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; active(from(X)) >= from(active(X)) ; first(mark(X1),X2) >= mark(first(X1,X2)) ; first(ok(X1),ok(X2)) >= ok(first(X1,X2)) ; first(X1,mark(X2)) >= mark(first(X1,X2)) ; cons(mark(X1),X2) >= mark(cons(X1,X2)) ; cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ; s(mark(X)) >= mark(s(X)) ; s(ok(X)) >= ok(s(X)) ; from(mark(X)) >= mark(from(X)) ; from(ok(X)) >= ok(from(X)) ; proper(nil) >= ok(nil) ; proper(first(X1,X2)) >= first(proper(X1),proper(X2)) ; proper(0) >= ok(0) ; proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ; proper(s(X)) >= s(proper(X)) ; proper(from(X)) >= from(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: active(first(0,X)) >= mark(nil) constraint: active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) constraint: active(first(X1,X2)) >= first(active(X1),X2) constraint: active(first(X1,X2)) >= first(X1,active(X2)) constraint: active(cons(X1,X2)) >= cons(active(X1),X2) constraint: active(s(X)) >= s(active(X)) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: active(from(X)) >= from(active(X)) constraint: first(mark(X1),X2) >= mark(first(X1,X2)) constraint: first(ok(X1),ok(X2)) >= ok(first(X1,X2)) constraint: first(X1,mark(X2)) >= mark(first(X1,X2)) constraint: cons(mark(X1),X2) >= mark(cons(X1,X2)) constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) constraint: s(mark(X)) >= mark(s(X)) constraint: s(ok(X)) >= ok(s(X)) constraint: from(mark(X)) >= mark(from(X)) constraint: from(ok(X)) >= ok(from(X)) constraint: proper(nil) >= ok(nil) constraint: proper(first(X1,X2)) >= first(proper(X1),proper(X2)) constraint: proper(0) >= ok(0) constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) constraint: proper(s(X)) >= s(proper(X)) constraint: proper(from(X)) >= from(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 1 components: { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_first -> 1 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(first(0,X)) -> mark(nil) [2] active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) [3] active(from(X)) -> mark(cons(X,from(s(X)))) [4] active(first(X1,X2)) -> first(active(X1),X2) [5] active(first(X1,X2)) -> first(X1,active(X2)) [6] active(s(X)) -> s(active(X)) [7] active(cons(X1,X2)) -> cons(active(X1),X2) [8] active(from(X)) -> from(active(X)) [9] first(mark(X1),X2) -> mark(first(X1,X2)) [10] first(X1,mark(X2)) -> mark(first(X1,X2)) [11] s(mark(X)) -> mark(s(X)) [12] cons(mark(X1),X2) -> mark(cons(X1,X2)) [13] from(mark(X)) -> mark(from(X)) [14] proper(first(X1,X2)) -> first(proper(X1),proper(X2)) [15] proper(0) -> ok(0) [16] proper(nil) -> ok(nil) [17] proper(s(X)) -> s(proper(X)) [18] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) [19] proper(from(X)) -> from(proper(X)) [20] first(ok(X1),ok(X2)) -> ok(first(X1,X2)) [21] s(ok(X)) -> ok(s(X)) [22] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) [23] from(ok(X)) -> ok(from(X)) [24] top(mark(X)) -> top(proper(X)) [25] top(ok(X)) -> top(active(X)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0 + 1; [ proper ] (X0) = 1*X0; [ 0 ] () = 0; [ active ] (X0) = 1*X0; [ top ] (X0) = 0; [ s ] (X0) = 2*X0; [ nil ] () = 0; [ ok ] (X0) = 1*X0; [ cons ] (X0,X1) = 2*X0; [ first ] (X0,X1) = 2*X1 + 2*X0 + 2; [ Marked_top ] (X0) = 2*X0; [ from ] (X0) = 2*X0 + 1; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ mark ] (X0) = 0; [ proper ] (X0) = 3*X0 + 0; [ 0 ] () = 3 + 0; [ active ] (X0) = 2*X0 + 0; [ top ] (X0) = 0; [ s ] (X0) = 1*X0 + 0; [ nil ] () = 2 + 0; [ ok ] (X0) = 2 + 2*X0 + 0; [ cons ] (X0,X1) = 1 + 1*X0 + 3*X1 + 0; [ first ] (X0,X1) = 2*X1 + 0; [ Marked_top ] (X0) = 2*X0 + 0; [ from ] (X0) = 2*X0 + 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 0.264114 seconds (real time) Cime Exit Status: 0