- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] dx(X) -> one [2] dx(a) -> zero [3] dx(plus(ALPHA,BETA)) -> plus(dx(ALPHA),dx(BETA)) [4] dx(times(ALPHA,BETA)) -> plus(times(BETA,dx(ALPHA)),times(ALPHA,dx(BETA))) [5] dx(minus(ALPHA,BETA)) -> minus(dx(ALPHA),dx(BETA)) [6] dx(neg(ALPHA)) -> neg(dx(ALPHA)) [7] dx(div(ALPHA,BETA)) -> minus(div(dx(ALPHA),BETA),times(ALPHA,div(dx(BETA),exp(BETA,two)))) [8] dx(ln(ALPHA)) -> div(dx(ALPHA),ALPHA) [9] dx(exp(ALPHA,BETA)) -> plus(times(BETA,times(exp(ALPHA,minus(BETA,one)),dx(ALPHA))), times(exp(ALPHA,BETA),times(ln(ALPHA),dx(BETA)))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { dx(a) >= zero ; dx(plus(ALPHA,BETA)) >= plus(dx(ALPHA),dx(BETA)) ; dx(times(ALPHA,BETA)) >= plus(times(BETA,dx(ALPHA)),times(ALPHA,dx(BETA))) ; dx(minus(ALPHA,BETA)) >= minus(dx(ALPHA),dx(BETA)) ; dx(neg(ALPHA)) >= neg(dx(ALPHA)) ; dx(div(ALPHA,BETA)) >= minus(div(dx(ALPHA),BETA), times(ALPHA,div(dx(BETA),exp(BETA,two)))) ; dx(exp(ALPHA,BETA)) >= plus(times(BETA, times(exp(ALPHA,minus(BETA,one)),dx(ALPHA))), times(exp(ALPHA,BETA),times(ln(ALPHA),dx(BETA)))) ; dx(ln(ALPHA)) >= div(dx(ALPHA),ALPHA) ; dx(X) >= one ; Marked_dx(plus(ALPHA,BETA)) >= Marked_dx(ALPHA) ; Marked_dx(plus(ALPHA,BETA)) >= Marked_dx(BETA) ; Marked_dx(times(ALPHA,BETA)) >= Marked_dx(ALPHA) ; Marked_dx(times(ALPHA,BETA)) >= Marked_dx(BETA) ; Marked_dx(minus(ALPHA,BETA)) >= Marked_dx(ALPHA) ; Marked_dx(minus(ALPHA,BETA)) >= Marked_dx(BETA) ; Marked_dx(neg(ALPHA)) >= Marked_dx(ALPHA) ; Marked_dx(div(ALPHA,BETA)) >= Marked_dx(ALPHA) ; Marked_dx(div(ALPHA,BETA)) >= Marked_dx(BETA) ; Marked_dx(exp(ALPHA,BETA)) >= Marked_dx(ALPHA) ; Marked_dx(exp(ALPHA,BETA)) >= Marked_dx(BETA) ; Marked_dx(ln(ALPHA)) >= Marked_dx(ALPHA) ; } + Disjunctions:{ { Marked_dx(plus(ALPHA,BETA)) > Marked_dx(ALPHA) ; } { Marked_dx(plus(ALPHA,BETA)) > Marked_dx(BETA) ; } { Marked_dx(times(ALPHA,BETA)) > Marked_dx(ALPHA) ; } { Marked_dx(times(ALPHA,BETA)) > Marked_dx(BETA) ; } { Marked_dx(minus(ALPHA,BETA)) > Marked_dx(ALPHA) ; } { Marked_dx(minus(ALPHA,BETA)) > Marked_dx(BETA) ; } { Marked_dx(neg(ALPHA)) > Marked_dx(ALPHA) ; } { Marked_dx(div(ALPHA,BETA)) > Marked_dx(ALPHA) ; } { Marked_dx(div(ALPHA,BETA)) > Marked_dx(BETA) ; } { Marked_dx(exp(ALPHA,BETA)) > Marked_dx(ALPHA) ; } { Marked_dx(exp(ALPHA,BETA)) > Marked_dx(BETA) ; } { Marked_dx(ln(ALPHA)) > Marked_dx(ALPHA) ; } } === 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 === === STOPING TIMER virtual === constraint: dx(a) >= zero constraint: dx(plus(ALPHA,BETA)) >= plus(dx(ALPHA),dx(BETA)) constraint: dx(times(ALPHA,BETA)) >= plus(times(BETA,dx(ALPHA)), times(ALPHA,dx(BETA))) constraint: dx(minus(ALPHA,BETA)) >= minus(dx(ALPHA),dx(BETA)) constraint: dx(neg(ALPHA)) >= neg(dx(ALPHA)) constraint: dx(div(ALPHA,BETA)) >= minus(div(dx(ALPHA),BETA), times(ALPHA,div(dx(BETA),exp(BETA,two)))) constraint: dx(exp(ALPHA,BETA)) >= plus(times(BETA, times(exp(ALPHA,minus(BETA,one)), dx(ALPHA))), times(exp(ALPHA,BETA), times(ln(ALPHA),dx(BETA)))) constraint: dx(ln(ALPHA)) >= div(dx(ALPHA),ALPHA) constraint: dx(X) >= one constraint: Marked_dx(plus(ALPHA,BETA)) >= Marked_dx(ALPHA) constraint: Marked_dx(plus(ALPHA,BETA)) >= Marked_dx(BETA) constraint: Marked_dx(times(ALPHA,BETA)) >= Marked_dx(ALPHA) constraint: Marked_dx(times(ALPHA,BETA)) >= Marked_dx(BETA) constraint: Marked_dx(minus(ALPHA,BETA)) >= Marked_dx(ALPHA) constraint: Marked_dx(minus(ALPHA,BETA)) >= Marked_dx(BETA) constraint: Marked_dx(neg(ALPHA)) >= Marked_dx(ALPHA) constraint: Marked_dx(div(ALPHA,BETA)) >= Marked_dx(ALPHA) constraint: Marked_dx(div(ALPHA,BETA)) >= Marked_dx(BETA) constraint: Marked_dx(exp(ALPHA,BETA)) >= Marked_dx(ALPHA) constraint: Marked_dx(exp(ALPHA,BETA)) >= Marked_dx(BETA) constraint: Marked_dx(ln(ALPHA)) >= Marked_dx(ALPHA) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] dx(X) -> one [2] dx(a) -> zero [3] dx(plus(ALPHA,BETA)) -> plus(dx(ALPHA),dx(BETA)) [4] dx(times(ALPHA,BETA)) -> plus(times(BETA,dx(ALPHA)),times(ALPHA,dx(BETA))) [5] dx(minus(ALPHA,BETA)) -> minus(dx(ALPHA),dx(BETA)) [6] dx(neg(ALPHA)) -> neg(dx(ALPHA)) [7] dx(div(ALPHA,BETA)) -> minus(div(dx(ALPHA),BETA),times(ALPHA,div(dx(BETA),exp(BETA,two)))) [8] dx(ln(ALPHA)) -> div(dx(ALPHA),ALPHA) [9] dx(exp(ALPHA,BETA)) -> plus(times(BETA,times(exp(ALPHA,minus(BETA,one)),dx(ALPHA))), times(exp(ALPHA,BETA),times(ln(ALPHA),dx(BETA)))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: RPO with AFS = AFS: and precedence: prec (All symbols are Lex.): { one < dx ; dx > one ; dx > zero ; dx > plus ; dx > times ; dx > minus ; dx > neg ; dx > div ; dx > exp ; dx > two ; dx > ln ; zero < dx ; plus < dx ; times < dx ; minus < dx ; neg < dx ; div < dx ; exp < dx ; two < dx ; ln < dx ; } ]} ]} ]} Cime worked for 0.183287 seconds (real time) Cime Exit Status: 0