- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] app(nil,k) -> k [2] app(l,nil) -> l [3] app(cons(x,l),k) -> cons(x,app(l,k)) [4] sum(cons(x,nil)) -> cons(x,nil) [5] sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) [6] sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) [7] plus(0,y) -> y [8] plus(s(x),y) -> s(plus(x,y)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 4 components: { --> } { --> } { --> } { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { app(nil,k) >= k ; app(cons(x,l),k) >= cons(x,app(l,k)) ; app(l,nil) >= l ; sum(app(l,cons(x,cons(y,k)))) >= sum(app(l,sum(cons(x,cons(y,k))))) ; sum(cons(x,nil)) >= cons(x,nil) ; sum(cons(x,cons(y,l))) >= sum(cons(plus(x,y),l)) ; plus(0,y) >= y ; plus(s(x),y) >= s(plus(x,y)) ; Marked_sum(app(l,cons(x,cons(y,k)))) >= Marked_sum(app(l, sum(cons(x,cons(y,k))))) ; } + Disjunctions:{ { Marked_sum(app(l,cons(x,cons(y,k)))) > Marked_sum(app(l, sum(cons(x,cons(y,k))))) ; } } === 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: app(nil,k) >= k constraint: app(cons(x,l),k) >= cons(x,app(l,k)) constraint: app(l,nil) >= l constraint: sum(app(l,cons(x,cons(y,k)))) >= sum(app(l,sum(cons(x,cons(y,k))))) constraint: sum(cons(x,nil)) >= cons(x,nil) constraint: sum(cons(x,cons(y,l))) >= sum(cons(plus(x,y),l)) constraint: plus(0,y) >= y constraint: plus(s(x),y) >= s(plus(x,y)) constraint: Marked_sum(app(l,cons(x,cons(y,k)))) >= Marked_sum(app(l, sum(cons( x, cons(y,k))))) APPLY CRITERIA (Subterm criterion) ST: Marked_app -> 1 APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { app(nil,k) >= k ; app(cons(x,l),k) >= cons(x,app(l,k)) ; app(l,nil) >= l ; sum(app(l,cons(x,cons(y,k)))) >= sum(app(l,sum(cons(x,cons(y,k))))) ; sum(cons(x,nil)) >= cons(x,nil) ; sum(cons(x,cons(y,l))) >= sum(cons(plus(x,y),l)) ; plus(0,y) >= y ; plus(s(x),y) >= s(plus(x,y)) ; Marked_sum(cons(x,cons(y,l))) >= Marked_sum(cons(plus(x,y),l)) ; } + Disjunctions:{ { Marked_sum(cons(x,cons(y,l))) > Marked_sum(cons(plus(x,y),l)) ; } } === 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: app(nil,k) >= k constraint: app(cons(x,l),k) >= cons(x,app(l,k)) constraint: app(l,nil) >= l constraint: sum(app(l,cons(x,cons(y,k)))) >= sum(app(l,sum(cons(x,cons(y,k))))) constraint: sum(cons(x,nil)) >= cons(x,nil) constraint: sum(cons(x,cons(y,l))) >= sum(cons(plus(x,y),l)) constraint: plus(0,y) >= y constraint: plus(s(x),y) >= s(plus(x,y)) constraint: Marked_sum(cons(x,cons(y,l))) >= Marked_sum(cons(plus(x,y),l)) APPLY CRITERIA (Subterm criterion) ST: Marked_plus -> 1 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: SOLVED { TRS termination of: [1] app(nil,k) -> k [2] app(l,nil) -> l [3] app(cons(x,l),k) -> cons(x,app(l,k)) [4] sum(cons(x,nil)) -> cons(x,nil) [5] sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) [6] sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) [7] plus(0,y) -> y [8] plus(s(x),y) -> s(plus(x,y)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ app ] (X0,X1) = 1*X0 + 1*X1 + 0; [ Marked_sum ] (X0) = 1*X0 + 0; [ plus ] (X0,X1) = 2 + 2*X1 + 0; [ cons ] (X0,X1) = 2 + 1*X1 + 0; [ s ] (X0) = 0; [ nil ] () = 0; [ 0 ] () = 3 + 0; [ sum ] (X0) = 3 + 0; ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ app ] (X0,X1) = 2*X0 + 2*X1 + 0; [ Marked_sum ] (X0) = 1*X0 + 0; [ plus ] (X0,X1) = 2 + 3*X0 + 1*X1 + 0; [ cons ] (X0,X1) = 1 + 1*X1 + 0; [ s ] (X0) = 3 + 1*X0 + 0; [ nil ] () = 0; [ 0 ] () = 2 + 0; [ sum ] (X0) = 1 + 0; ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 0.202523 seconds (real time) Cime Exit Status: 0