/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. !plus : [o * o] --> o 0 : [] --> o J1 : [o * o] --> o J2 : [o * o * o] --> o J3 : [o * o * o * o] --> o J4 : [o * o * o * o * o] --> o M : [o * o * o * o * o] --> o P : [o * o * o * o * o] --> o Q11 : [o * o] --> o Q21 : [o * o * o] --> o Q22 : [o * o * o] --> o Q31 : [o * o * o * o] --> o Q32 : [o * o * o * o] --> o Q33 : [o * o * o * o] --> o Q41 : [o * o * o * o * o] --> o Q42 : [o * o * o * o * o] --> o Q43 : [o * o * o * o * o] --> o Q44 : [o * o * o * o * o] --> o R1 : [o * o * o] --> o R2 : [o * o * o * o] --> o R3 : [o * o * o * o * o] --> o R4 : [o * o * o * o * o * o] --> o S : [o] --> o a : [o] --> o l : [o] --> o o : [o] --> o a(X) => X o(X) => X l(X) => X S(X) => X !plus(X, Y) => Y !plus(X, Y) => X P(X, Y, Z, U, V) => V P(X, Y, Z, U, V) => U P(X, Y, Z, U, V) => Z P(X, Y, Z, U, V) => Y P(X, Y, Z, U, V) => X M(X, Y, Z, U, V) => V M(X, Y, Z, U, V) => U M(X, Y, Z, U, V) => Z M(X, Y, Z, U, V) => Y M(X, Y, Z, U, V) => X J1(X, Y) => Y J1(X, Y) => X J2(X, Y, Z) => Z J2(X, Y, Z) => Y J2(X, Y, Z) => X J3(X, Y, Z, U) => U J3(X, Y, Z, U) => Z J3(X, Y, Z, U) => Y J3(X, Y, Z, U) => X J4(X, Y, Z, U, V) => V J4(X, Y, Z, U, V) => U J4(X, Y, Z, U, V) => Z J4(X, Y, Z, U, V) => Y J4(X, Y, Z, U, V) => X Q11(X, Y) => Y Q11(X, Y) => X Q21(X, Y, Z) => Z Q21(X, Y, Z) => Y Q21(X, Y, Z) => X Q22(X, Y, Z) => Z Q22(X, Y, Z) => Y Q22(X, Y, Z) => X Q31(X, Y, Z, U) => U Q31(X, Y, Z, U) => Z Q31(X, Y, Z, U) => Y Q31(X, Y, Z, U) => X Q32(X, Y, Z, U) => U Q32(X, Y, Z, U) => Z Q32(X, Y, Z, U) => Y Q32(X, Y, Z, U) => X Q33(X, Y, Z, U) => U Q33(X, Y, Z, U) => Z Q33(X, Y, Z, U) => Y Q33(X, Y, Z, U) => X Q41(X, Y, Z, U, V) => V Q41(X, Y, Z, U, V) => U Q41(X, Y, Z, U, V) => Z Q41(X, Y, Z, U, V) => Y Q41(X, Y, Z, U, V) => X Q42(X, Y, Z, U, V) => V Q42(X, Y, Z, U, V) => U Q42(X, Y, Z, U, V) => Z Q42(X, Y, Z, U, V) => Y Q42(X, Y, Z, U, V) => X Q43(X, Y, Z, U, V) => V Q43(X, Y, Z, U, V) => U Q43(X, Y, Z, U, V) => Z Q43(X, Y, Z, U, V) => Y Q43(X, Y, Z, U, V) => X Q44(X, Y, Z, U, V) => V Q44(X, Y, Z, U, V) => U Q44(X, Y, Z, U, V) => Z Q44(X, Y, Z, U, V) => Y Q44(X, Y, Z, U, V) => X R1(X, Y, Z) => Z R1(X, Y, Z) => Y R1(X, Y, Z) => X R2(X, Y, Z, U) => U R2(X, Y, Z, U) => Z R2(X, Y, Z, U) => Y R2(X, Y, Z, U) => X R3(X, Y, Z, U, V) => V R3(X, Y, Z, U, V) => U R3(X, Y, Z, U, V) => Z R3(X, Y, Z, U, V) => Y R3(X, Y, Z, U, V) => X R4(X, Y, Z, U, V, W) => W R4(X, Y, Z, U, V, W) => V R4(X, Y, Z, U, V, W) => U R4(X, Y, Z, U, V, W) => Z R4(X, Y, Z, U, V, W) => Y R4(X, Y, Z, U, V, W) => X P(0, 0, 0, 0, 0) => S(0) !plus(X, S(Y)) => S(!plus(X, Y)) a(l(X)) => l(a(a(X))) l(o(X)) => o(l(l(X))) o(X) => l(X) l(X) => a(X) a(S(X)) => S(l(X)) a(!plus(X, Y)) => !plus(l(X), Y) a(!plus(X, Y)) => !plus(X, l(Y)) a(P(X, Y, Z, U, V)) => P(X, Y, Z, U, l(V)) a(P(X, Y, Z, U, V)) => P(X, Y, Z, l(U), V) a(P(X, Y, Z, U, V)) => P(X, Y, l(Z), U, V) a(P(X, Y, Z, U, V)) => P(X, l(Y), Z, U, V) a(P(X, Y, Z, U, V)) => P(l(X), Y, Z, U, V) !plus(X, o(Y)) => o(!plus(X, Y)) P(X, Y, Z, U, o(V)) => o(P(X, Y, Z, U, V)) P(X, Y, Z, o(U), V) => o(P(X, Y, Z, U, V)) P(X, Y, o(Z), U, V) => o(P(X, Y, Z, U, V)) P(X, o(Y), Z, U, V) => o(P(X, Y, Z, U, V)) P(o(X), Y, Z, U, V) => o(P(X, Y, Z, U, V)) M(X, Y, Z, U, l(V)) => !plus(M(X, Y, Z, U, V), P(X, Y, Z, U, V)) J4(X, Y, Z, l(U), V) => P(X, Y, Z, J4(X, Y, Z, U, V), 0) J3(X, Y, l(Z), U) => P(X, Y, J3(X, Y, Z, U), 0, 0) J2(X, l(Y), Z) => P(X, J2(X, Y, Z), 0, 0, 0) J1(l(X), Y) => P(J1(X, Y), 0, 0, 0, 0) a(S(X)) => o(X) P(0, 0, 0, 0, S(X)) => o(M(0, 0, 0, 0, X)) P(0, 0, 0, 0, P(X, Y, Z, U, V)) => o(M(X, Y, Z, U, V)) P(X, Y, Z, S(U), V) => o(J4(X, Y, Z, U, V)) P(X, Y, S(Z), 0, U) => o(J3(X, Y, Z, U)) P(X, S(Y), 0, 0, Z) => o(J2(X, Y, Z)) P(S(X), 0, 0, 0, Y) => o(J1(X, Y)) P(X, Y, Z, S(U), S(V)) => o(J4(X, Y, Z, U, P(X, Y, Z, S(U), V))) P(X, Y, S(Z), 0, S(U)) => o(J3(X, Y, Z, P(X, Y, S(Z), 0, U))) P(X, S(Y), 0, 0, S(Z)) => o(J2(X, Y, P(X, S(Y), 0, 0, Z))) P(S(X), 0, 0, 0, S(Y)) => o(J1(X, P(S(X), 0, 0, 0, Y))) a(P(X, Y, Z, U, 0)) => Q44(X, Y, Z, a(U), U) a(P(X, Y, Z, U, 0)) => Q43(X, Y, Z, a(U), Z) a(P(X, Y, Z, U, 0)) => Q42(X, Y, Z, a(U), Y) a(P(X, Y, Z, U, 0)) => Q41(X, Y, Z, a(U), X) a(P(X, Y, Z, 0, 0)) => Q33(X, Y, a(Z), Z) a(P(X, Y, Z, 0, 0)) => Q32(X, Y, a(Z), Y) a(P(X, Y, Z, 0, 0)) => Q31(X, Y, a(Z), X) a(P(X, Y, 0, 0, 0)) => Q22(X, a(Y), Y) a(P(X, Y, 0, 0, 0)) => Q21(X, a(Y), X) a(P(X, 0, 0, 0, 0)) => Q11(a(X), X) Q44(X, Y, Z, o(U), V) => o(P(X, Y, Z, U, V)) Q43(X, Y, Z, o(U), V) => o(P(X, Y, Z, U, V)) Q42(X, Y, Z, o(U), V) => o(P(X, Y, Z, U, V)) Q41(X, Y, Z, o(U), V) => o(P(X, Y, Z, U, V)) Q33(X, Y, o(Z), U) => o(P(X, Y, Z, 0, U)) Q32(X, Y, o(Z), U) => o(P(X, Y, Z, 0, U)) Q31(X, Y, o(Z), U) => o(P(X, Y, Z, 0, U)) Q22(X, o(Y), Z) => o(P(X, Y, 0, 0, Z)) Q21(X, o(Y), Z) => o(P(X, Y, 0, 0, Z)) Q11(o(X), Y) => o(P(X, 0, 0, 0, Y)) a(P(X, Y, Z, U, S(V))) => R4(X, Y, Z, a(U), U, V) a(P(X, Y, Z, 0, S(U))) => R3(X, Y, a(Z), Z, U) a(P(X, Y, 0, 0, S(Z))) => R2(X, a(Y), Y, Z) a(P(X, 0, 0, 0, S(Y))) => R1(a(X), X, Y) R4(X, Y, Z, o(U), V, W) => o(P(X, Y, Z, U, P(X, Y, Z, V, W))) R3(X, Y, o(Z), U, V) => o(P(X, Y, Z, 0, P(X, Y, U, 0, V))) R2(X, o(Y), Z, U) => o(P(X, Y, 0, 0, P(X, Z, 0, 0, U))) R1(o(X), Y, Z) => o(P(X, 0, 0, 0, P(Y, 0, 0, 0, Z)))