- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] norm(nil) -> 0 [2] norm(g(x,y)) -> s(norm(x)) [3] f(x,nil) -> g(nil,x) [4] f(x,g(y,z)) -> g(f(x,y),z) [5] rem(nil,y) -> nil [6] rem(g(x,y),0) -> g(x,y) [7] rem(g(x,y),s(z)) -> rem(x,z) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 3 components: { --> } { --> } { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { norm(nil) >= 0 ; norm(g(x,y)) >= s(norm(x)) ; f(x,nil) >= g(nil,x) ; f(x,g(y,z)) >= g(f(x,y),z) ; rem(nil,y) >= nil ; rem(g(x,y),0) >= g(x,y) ; rem(g(x,y),s(z)) >= rem(x,z) ; Marked_norm(g(x,y)) >= Marked_norm(x) ; } + Disjunctions:{ { Marked_norm(g(x,y)) > Marked_norm(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: norm(nil) >= 0 constraint: norm(g(x,y)) >= s(norm(x)) constraint: f(x,nil) >= g(nil,x) constraint: f(x,g(y,z)) >= g(f(x,y),z) constraint: rem(nil,y) >= nil constraint: rem(g(x,y),0) >= g(x,y) constraint: rem(g(x,y),s(z)) >= rem(x,z) constraint: Marked_norm(g(x,y)) >= Marked_norm(x) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { norm(nil) >= 0 ; norm(g(x,y)) >= s(norm(x)) ; f(x,nil) >= g(nil,x) ; f(x,g(y,z)) >= g(f(x,y),z) ; rem(nil,y) >= nil ; rem(g(x,y),0) >= g(x,y) ; rem(g(x,y),s(z)) >= rem(x,z) ; Marked_f(x,g(y,z)) >= Marked_f(x,y) ; } + Disjunctions:{ { Marked_f(x,g(y,z)) > Marked_f(x,y) ; } } === 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: norm(nil) >= 0 constraint: norm(g(x,y)) >= s(norm(x)) constraint: f(x,nil) >= g(nil,x) constraint: f(x,g(y,z)) >= g(f(x,y),z) constraint: rem(nil,y) >= nil constraint: rem(g(x,y),0) >= g(x,y) constraint: rem(g(x,y),s(z)) >= rem(x,z) constraint: Marked_f(x,g(y,z)) >= Marked_f(x,y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { norm(nil) >= 0 ; norm(g(x,y)) >= s(norm(x)) ; f(x,nil) >= g(nil,x) ; f(x,g(y,z)) >= g(f(x,y),z) ; rem(nil,y) >= nil ; rem(g(x,y),0) >= g(x,y) ; rem(g(x,y),s(z)) >= rem(x,z) ; Marked_rem(g(x,y),s(z)) >= Marked_rem(x,z) ; } + Disjunctions:{ { Marked_rem(g(x,y),s(z)) > Marked_rem(x,z) ; } } === 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: norm(nil) >= 0 constraint: norm(g(x,y)) >= s(norm(x)) constraint: f(x,nil) >= g(nil,x) constraint: f(x,g(y,z)) >= g(f(x,y),z) constraint: rem(nil,y) >= nil constraint: rem(g(x,y),0) >= g(x,y) constraint: rem(g(x,y),s(z)) >= rem(x,z) constraint: Marked_rem(g(x,y),s(z)) >= Marked_rem(x,z) 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] norm(nil) -> 0 [2] norm(g(x,y)) -> s(norm(x)) [3] f(x,nil) -> g(nil,x) [4] f(x,g(y,z)) -> g(f(x,y),z) [5] rem(nil,y) -> nil [6] rem(g(x,y),0) -> g(x,y) [7] rem(g(x,y),s(z)) -> rem(x,z) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ g ] (X0,X1) = 1 + 3*X0 + 0; [ nil ] () = 0; [ rem ] (X0,X1) = 1*X0 + 0; [ norm ] (X0) = 2*X0 + 0; [ Marked_norm ] (X0) = 3*X0 + 0; [ f ] (X0,X1) = 1 + 3*X1 + 0; [ s ] (X0) = 2 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ Marked_f ] (X0,X1) = 3*X1 + 0; [ g ] (X0,X1) = 2 + 3*X0 + 0; [ nil ] () = 0; [ rem ] (X0,X1) = 1*X0 + 0; [ norm ] (X0) = 2 + 2*X0 + 0; [ f ] (X0,X1) = 2 + 3*X1 + 0; [ s ] (X0) = 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ g ] (X0,X1) = 2 + 2*X0 + 0; [ nil ] () = 0; [ rem ] (X0,X1) = 2*X0 + 0; [ norm ] (X0) = 1 + 2*X0 + 0; [ f ] (X0,X1) = 2 + 2*X1 + 0; [ s ] (X0) = 1 + 1*X0 + 0; [ Marked_rem ] (X0,X1) = 1*X1 + 0; ]} ]} ]} Cime worked for 0.065569 seconds (real time) Cime Exit Status: 0