Problem Secret 05 TRS cime5

LMPO

Execution Time (secs)
0.910
Answer
MAYBE
InputSecret 05 TRS cime5
MAYBE

We consider the following Problem:

  Strict Trs:
    {  intersect'ii'in(cons(X, X0), cons(X, X1)) -> intersect'ii'out()
     , intersect'ii'in(Xs, cons(X0, Ys)) ->
       u'1'1(intersect'ii'in(Xs, Ys))
     , u'1'1(intersect'ii'out()) -> intersect'ii'out()
     , intersect'ii'in(cons(X0, Xs), Ys) ->
       u'2'1(intersect'ii'in(Xs, Ys))
     , u'2'1(intersect'ii'out()) -> intersect'ii'out()
     , reduce'ii'in(sequent(cons(if(A, B), Fs), Gs), NF) ->
       u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B), A), Fs), Gs), NF))
     , u'3'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(iff(A, B), Fs), Gs), NF) ->
       u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A, B), if(B, A)), Fs), Gs),
                          NF))
     , u'4'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2a(F1, F2), Fs), Gs), NF) ->
       u'5'1(reduce'ii'in(sequent(cons(F1, cons(F2, Fs)), Gs), NF))
     , u'5'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2b(F1, F2), Fs), Gs), NF) ->
       u'6'1(reduce'ii'in(sequent(cons(F1, Fs), Gs), NF), F2, Fs, Gs, NF)
     , u'6'1(reduce'ii'out(), F2, Fs, Gs, NF) ->
       u'6'2(reduce'ii'in(sequent(cons(F2, Fs), Gs), NF))
     , u'6'2(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2d(F1), Fs), Gs), NF) ->
       u'7'1(reduce'ii'in(sequent(Fs, cons(F1, Gs)), NF))
     , u'7'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(if(A, B), Gs)), NF) ->
       u'8'1(reduce'ii'in(sequent(Fs, cons(x'2b(x'2d(B), A), Gs)), NF))
     , u'8'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(iff(A, B), Gs)), NF) ->
       u'9'1(reduce'ii'in(sequent(Fs, cons(x'2a(if(A, B), if(B, A)), Gs)),
                          NF))
     , u'9'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(p(V), Fs), Gs), sequent(Left, Right))
       ->
       u'10'1(reduce'ii'in(sequent(Fs, Gs),
                           sequent(cons(p(V), Left), Right)))
     , u'10'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2b(G1, G2), Gs)), NF) ->
       u'11'1(reduce'ii'in(sequent(Fs, cons(G1, cons(G2, Gs))), NF))
     , u'11'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2a(G1, G2), Gs)), NF) ->
       u'12'1(reduce'ii'in(sequent(Fs, cons(G1, Gs)), NF), Fs, G2, Gs, NF)
     , u'12'1(reduce'ii'out(), Fs, G2, Gs, NF) ->
       u'12'2(reduce'ii'in(sequent(Fs, cons(G2, Gs)), NF))
     , u'12'2(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2d(G1), Gs)), NF) ->
       u'13'1(reduce'ii'in(sequent(cons(G1, Fs), Gs), NF))
     , u'13'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(nil(), cons(p(V), Gs)),
                    sequent(Left, Right))
       ->
       u'14'1(reduce'ii'in(sequent(nil(), Gs),
                           sequent(Left, cons(p(V), Right))))
     , u'14'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(nil(), nil()), sequent(F1, F2)) ->
       u'15'1(intersect'ii'in(F1, F2))
     , u'15'1(intersect'ii'out()) -> reduce'ii'out()
     , tautology'i'in(F) ->
       u'16'1(reduce'ii'in(sequent(nil(), cons(F, nil())),
                           sequent(nil(), nil())))
     , u'16'1(reduce'ii'out()) -> tautology'i'out()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)
1.323
Answer
MAYBE
InputSecret 05 TRS cime5
MAYBE

We consider the following Problem:

  Strict Trs:
    {  intersect'ii'in(cons(X, X0), cons(X, X1)) -> intersect'ii'out()
     , intersect'ii'in(Xs, cons(X0, Ys)) ->
       u'1'1(intersect'ii'in(Xs, Ys))
     , u'1'1(intersect'ii'out()) -> intersect'ii'out()
     , intersect'ii'in(cons(X0, Xs), Ys) ->
       u'2'1(intersect'ii'in(Xs, Ys))
     , u'2'1(intersect'ii'out()) -> intersect'ii'out()
     , reduce'ii'in(sequent(cons(if(A, B), Fs), Gs), NF) ->
       u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B), A), Fs), Gs), NF))
     , u'3'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(iff(A, B), Fs), Gs), NF) ->
       u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A, B), if(B, A)), Fs), Gs),
                          NF))
     , u'4'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2a(F1, F2), Fs), Gs), NF) ->
       u'5'1(reduce'ii'in(sequent(cons(F1, cons(F2, Fs)), Gs), NF))
     , u'5'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2b(F1, F2), Fs), Gs), NF) ->
       u'6'1(reduce'ii'in(sequent(cons(F1, Fs), Gs), NF), F2, Fs, Gs, NF)
     , u'6'1(reduce'ii'out(), F2, Fs, Gs, NF) ->
       u'6'2(reduce'ii'in(sequent(cons(F2, Fs), Gs), NF))
     , u'6'2(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2d(F1), Fs), Gs), NF) ->
       u'7'1(reduce'ii'in(sequent(Fs, cons(F1, Gs)), NF))
     , u'7'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(if(A, B), Gs)), NF) ->
       u'8'1(reduce'ii'in(sequent(Fs, cons(x'2b(x'2d(B), A), Gs)), NF))
     , u'8'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(iff(A, B), Gs)), NF) ->
       u'9'1(reduce'ii'in(sequent(Fs, cons(x'2a(if(A, B), if(B, A)), Gs)),
                          NF))
     , u'9'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(p(V), Fs), Gs), sequent(Left, Right))
       ->
       u'10'1(reduce'ii'in(sequent(Fs, Gs),
                           sequent(cons(p(V), Left), Right)))
     , u'10'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2b(G1, G2), Gs)), NF) ->
       u'11'1(reduce'ii'in(sequent(Fs, cons(G1, cons(G2, Gs))), NF))
     , u'11'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2a(G1, G2), Gs)), NF) ->
       u'12'1(reduce'ii'in(sequent(Fs, cons(G1, Gs)), NF), Fs, G2, Gs, NF)
     , u'12'1(reduce'ii'out(), Fs, G2, Gs, NF) ->
       u'12'2(reduce'ii'in(sequent(Fs, cons(G2, Gs)), NF))
     , u'12'2(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2d(G1), Gs)), NF) ->
       u'13'1(reduce'ii'in(sequent(cons(G1, Fs), Gs), NF))
     , u'13'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(nil(), cons(p(V), Gs)),
                    sequent(Left, Right))
       ->
       u'14'1(reduce'ii'in(sequent(nil(), Gs),
                           sequent(Left, cons(p(V), Right))))
     , u'14'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(nil(), nil()), sequent(F1, F2)) ->
       u'15'1(intersect'ii'in(F1, F2))
     , u'15'1(intersect'ii'out()) -> reduce'ii'out()
     , tautology'i'in(F) ->
       u'16'1(reduce'ii'in(sequent(nil(), cons(F, nil())),
                           sequent(nil(), nil())))
     , u'16'1(reduce'ii'out()) -> tautology'i'out()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)
0.856
Answer
MAYBE
InputSecret 05 TRS cime5
MAYBE

We consider the following Problem:

  Strict Trs:
    {  intersect'ii'in(cons(X, X0), cons(X, X1)) -> intersect'ii'out()
     , intersect'ii'in(Xs, cons(X0, Ys)) ->
       u'1'1(intersect'ii'in(Xs, Ys))
     , u'1'1(intersect'ii'out()) -> intersect'ii'out()
     , intersect'ii'in(cons(X0, Xs), Ys) ->
       u'2'1(intersect'ii'in(Xs, Ys))
     , u'2'1(intersect'ii'out()) -> intersect'ii'out()
     , reduce'ii'in(sequent(cons(if(A, B), Fs), Gs), NF) ->
       u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B), A), Fs), Gs), NF))
     , u'3'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(iff(A, B), Fs), Gs), NF) ->
       u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A, B), if(B, A)), Fs), Gs),
                          NF))
     , u'4'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2a(F1, F2), Fs), Gs), NF) ->
       u'5'1(reduce'ii'in(sequent(cons(F1, cons(F2, Fs)), Gs), NF))
     , u'5'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2b(F1, F2), Fs), Gs), NF) ->
       u'6'1(reduce'ii'in(sequent(cons(F1, Fs), Gs), NF), F2, Fs, Gs, NF)
     , u'6'1(reduce'ii'out(), F2, Fs, Gs, NF) ->
       u'6'2(reduce'ii'in(sequent(cons(F2, Fs), Gs), NF))
     , u'6'2(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2d(F1), Fs), Gs), NF) ->
       u'7'1(reduce'ii'in(sequent(Fs, cons(F1, Gs)), NF))
     , u'7'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(if(A, B), Gs)), NF) ->
       u'8'1(reduce'ii'in(sequent(Fs, cons(x'2b(x'2d(B), A), Gs)), NF))
     , u'8'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(iff(A, B), Gs)), NF) ->
       u'9'1(reduce'ii'in(sequent(Fs, cons(x'2a(if(A, B), if(B, A)), Gs)),
                          NF))
     , u'9'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(p(V), Fs), Gs), sequent(Left, Right))
       ->
       u'10'1(reduce'ii'in(sequent(Fs, Gs),
                           sequent(cons(p(V), Left), Right)))
     , u'10'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2b(G1, G2), Gs)), NF) ->
       u'11'1(reduce'ii'in(sequent(Fs, cons(G1, cons(G2, Gs))), NF))
     , u'11'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2a(G1, G2), Gs)), NF) ->
       u'12'1(reduce'ii'in(sequent(Fs, cons(G1, Gs)), NF), Fs, G2, Gs, NF)
     , u'12'1(reduce'ii'out(), Fs, G2, Gs, NF) ->
       u'12'2(reduce'ii'in(sequent(Fs, cons(G2, Gs)), NF))
     , u'12'2(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2d(G1), Gs)), NF) ->
       u'13'1(reduce'ii'in(sequent(cons(G1, Fs), Gs), NF))
     , u'13'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(nil(), cons(p(V), Gs)),
                    sequent(Left, Right))
       ->
       u'14'1(reduce'ii'in(sequent(nil(), Gs),
                           sequent(Left, cons(p(V), Right))))
     , u'14'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(nil(), nil()), sequent(F1, F2)) ->
       u'15'1(intersect'ii'in(F1, F2))
     , u'15'1(intersect'ii'out()) -> reduce'ii'out()
     , tautology'i'in(F) ->
       u'16'1(reduce'ii'in(sequent(nil(), cons(F, nil())),
                           sequent(nil(), nil())))
     , u'16'1(reduce'ii'out()) -> tautology'i'out()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)
0.806
Answer
MAYBE
InputSecret 05 TRS cime5
MAYBE

We consider the following Problem:

  Strict Trs:
    {  intersect'ii'in(cons(X, X0), cons(X, X1)) -> intersect'ii'out()
     , intersect'ii'in(Xs, cons(X0, Ys)) ->
       u'1'1(intersect'ii'in(Xs, Ys))
     , u'1'1(intersect'ii'out()) -> intersect'ii'out()
     , intersect'ii'in(cons(X0, Xs), Ys) ->
       u'2'1(intersect'ii'in(Xs, Ys))
     , u'2'1(intersect'ii'out()) -> intersect'ii'out()
     , reduce'ii'in(sequent(cons(if(A, B), Fs), Gs), NF) ->
       u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B), A), Fs), Gs), NF))
     , u'3'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(iff(A, B), Fs), Gs), NF) ->
       u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A, B), if(B, A)), Fs), Gs),
                          NF))
     , u'4'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2a(F1, F2), Fs), Gs), NF) ->
       u'5'1(reduce'ii'in(sequent(cons(F1, cons(F2, Fs)), Gs), NF))
     , u'5'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2b(F1, F2), Fs), Gs), NF) ->
       u'6'1(reduce'ii'in(sequent(cons(F1, Fs), Gs), NF), F2, Fs, Gs, NF)
     , u'6'1(reduce'ii'out(), F2, Fs, Gs, NF) ->
       u'6'2(reduce'ii'in(sequent(cons(F2, Fs), Gs), NF))
     , u'6'2(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2d(F1), Fs), Gs), NF) ->
       u'7'1(reduce'ii'in(sequent(Fs, cons(F1, Gs)), NF))
     , u'7'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(if(A, B), Gs)), NF) ->
       u'8'1(reduce'ii'in(sequent(Fs, cons(x'2b(x'2d(B), A), Gs)), NF))
     , u'8'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(iff(A, B), Gs)), NF) ->
       u'9'1(reduce'ii'in(sequent(Fs, cons(x'2a(if(A, B), if(B, A)), Gs)),
                          NF))
     , u'9'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(p(V), Fs), Gs), sequent(Left, Right))
       ->
       u'10'1(reduce'ii'in(sequent(Fs, Gs),
                           sequent(cons(p(V), Left), Right)))
     , u'10'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2b(G1, G2), Gs)), NF) ->
       u'11'1(reduce'ii'in(sequent(Fs, cons(G1, cons(G2, Gs))), NF))
     , u'11'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2a(G1, G2), Gs)), NF) ->
       u'12'1(reduce'ii'in(sequent(Fs, cons(G1, Gs)), NF), Fs, G2, Gs, NF)
     , u'12'1(reduce'ii'out(), Fs, G2, Gs, NF) ->
       u'12'2(reduce'ii'in(sequent(Fs, cons(G2, Gs)), NF))
     , u'12'2(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2d(G1), Gs)), NF) ->
       u'13'1(reduce'ii'in(sequent(cons(G1, Fs), Gs), NF))
     , u'13'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(nil(), cons(p(V), Gs)),
                    sequent(Left, Right))
       ->
       u'14'1(reduce'ii'in(sequent(nil(), Gs),
                           sequent(Left, cons(p(V), Right))))
     , u'14'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(nil(), nil()), sequent(F1, F2)) ->
       u'15'1(intersect'ii'in(F1, F2))
     , u'15'1(intersect'ii'out()) -> reduce'ii'out()
     , tautology'i'in(F) ->
       u'16'1(reduce'ii'in(sequent(nil(), cons(F, nil())),
                           sequent(nil(), nil())))
     , u'16'1(reduce'ii'out()) -> tautology'i'out()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)
0.833
Answer
MAYBE
InputSecret 05 TRS cime5
MAYBE

We consider the following Problem:

  Strict Trs:
    {  intersect'ii'in(cons(X, X0), cons(X, X1)) -> intersect'ii'out()
     , intersect'ii'in(Xs, cons(X0, Ys)) ->
       u'1'1(intersect'ii'in(Xs, Ys))
     , u'1'1(intersect'ii'out()) -> intersect'ii'out()
     , intersect'ii'in(cons(X0, Xs), Ys) ->
       u'2'1(intersect'ii'in(Xs, Ys))
     , u'2'1(intersect'ii'out()) -> intersect'ii'out()
     , reduce'ii'in(sequent(cons(if(A, B), Fs), Gs), NF) ->
       u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B), A), Fs), Gs), NF))
     , u'3'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(iff(A, B), Fs), Gs), NF) ->
       u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A, B), if(B, A)), Fs), Gs),
                          NF))
     , u'4'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2a(F1, F2), Fs), Gs), NF) ->
       u'5'1(reduce'ii'in(sequent(cons(F1, cons(F2, Fs)), Gs), NF))
     , u'5'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2b(F1, F2), Fs), Gs), NF) ->
       u'6'1(reduce'ii'in(sequent(cons(F1, Fs), Gs), NF), F2, Fs, Gs, NF)
     , u'6'1(reduce'ii'out(), F2, Fs, Gs, NF) ->
       u'6'2(reduce'ii'in(sequent(cons(F2, Fs), Gs), NF))
     , u'6'2(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2d(F1), Fs), Gs), NF) ->
       u'7'1(reduce'ii'in(sequent(Fs, cons(F1, Gs)), NF))
     , u'7'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(if(A, B), Gs)), NF) ->
       u'8'1(reduce'ii'in(sequent(Fs, cons(x'2b(x'2d(B), A), Gs)), NF))
     , u'8'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(iff(A, B), Gs)), NF) ->
       u'9'1(reduce'ii'in(sequent(Fs, cons(x'2a(if(A, B), if(B, A)), Gs)),
                          NF))
     , u'9'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(p(V), Fs), Gs), sequent(Left, Right))
       ->
       u'10'1(reduce'ii'in(sequent(Fs, Gs),
                           sequent(cons(p(V), Left), Right)))
     , u'10'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2b(G1, G2), Gs)), NF) ->
       u'11'1(reduce'ii'in(sequent(Fs, cons(G1, cons(G2, Gs))), NF))
     , u'11'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2a(G1, G2), Gs)), NF) ->
       u'12'1(reduce'ii'in(sequent(Fs, cons(G1, Gs)), NF), Fs, G2, Gs, NF)
     , u'12'1(reduce'ii'out(), Fs, G2, Gs, NF) ->
       u'12'2(reduce'ii'in(sequent(Fs, cons(G2, Gs)), NF))
     , u'12'2(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2d(G1), Gs)), NF) ->
       u'13'1(reduce'ii'in(sequent(cons(G1, Fs), Gs), NF))
     , u'13'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(nil(), cons(p(V), Gs)),
                    sequent(Left, Right))
       ->
       u'14'1(reduce'ii'in(sequent(nil(), Gs),
                           sequent(Left, cons(p(V), Right))))
     , u'14'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(nil(), nil()), sequent(F1, F2)) ->
       u'15'1(intersect'ii'in(F1, F2))
     , u'15'1(intersect'ii'out()) -> reduce'ii'out()
     , tautology'i'in(F) ->
       u'16'1(reduce'ii'in(sequent(nil(), cons(F, nil())),
                           sequent(nil(), nil())))
     , u'16'1(reduce'ii'out()) -> tautology'i'out()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)
1.002
Answer
MAYBE
InputSecret 05 TRS cime5
MAYBE

We consider the following Problem:

  Strict Trs:
    {  intersect'ii'in(cons(X, X0), cons(X, X1)) -> intersect'ii'out()
     , intersect'ii'in(Xs, cons(X0, Ys)) ->
       u'1'1(intersect'ii'in(Xs, Ys))
     , u'1'1(intersect'ii'out()) -> intersect'ii'out()
     , intersect'ii'in(cons(X0, Xs), Ys) ->
       u'2'1(intersect'ii'in(Xs, Ys))
     , u'2'1(intersect'ii'out()) -> intersect'ii'out()
     , reduce'ii'in(sequent(cons(if(A, B), Fs), Gs), NF) ->
       u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B), A), Fs), Gs), NF))
     , u'3'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(iff(A, B), Fs), Gs), NF) ->
       u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A, B), if(B, A)), Fs), Gs),
                          NF))
     , u'4'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2a(F1, F2), Fs), Gs), NF) ->
       u'5'1(reduce'ii'in(sequent(cons(F1, cons(F2, Fs)), Gs), NF))
     , u'5'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2b(F1, F2), Fs), Gs), NF) ->
       u'6'1(reduce'ii'in(sequent(cons(F1, Fs), Gs), NF), F2, Fs, Gs, NF)
     , u'6'1(reduce'ii'out(), F2, Fs, Gs, NF) ->
       u'6'2(reduce'ii'in(sequent(cons(F2, Fs), Gs), NF))
     , u'6'2(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(x'2d(F1), Fs), Gs), NF) ->
       u'7'1(reduce'ii'in(sequent(Fs, cons(F1, Gs)), NF))
     , u'7'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(if(A, B), Gs)), NF) ->
       u'8'1(reduce'ii'in(sequent(Fs, cons(x'2b(x'2d(B), A), Gs)), NF))
     , u'8'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(iff(A, B), Gs)), NF) ->
       u'9'1(reduce'ii'in(sequent(Fs, cons(x'2a(if(A, B), if(B, A)), Gs)),
                          NF))
     , u'9'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(cons(p(V), Fs), Gs), sequent(Left, Right))
       ->
       u'10'1(reduce'ii'in(sequent(Fs, Gs),
                           sequent(cons(p(V), Left), Right)))
     , u'10'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2b(G1, G2), Gs)), NF) ->
       u'11'1(reduce'ii'in(sequent(Fs, cons(G1, cons(G2, Gs))), NF))
     , u'11'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2a(G1, G2), Gs)), NF) ->
       u'12'1(reduce'ii'in(sequent(Fs, cons(G1, Gs)), NF), Fs, G2, Gs, NF)
     , u'12'1(reduce'ii'out(), Fs, G2, Gs, NF) ->
       u'12'2(reduce'ii'in(sequent(Fs, cons(G2, Gs)), NF))
     , u'12'2(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(Fs, cons(x'2d(G1), Gs)), NF) ->
       u'13'1(reduce'ii'in(sequent(cons(G1, Fs), Gs), NF))
     , u'13'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(nil(), cons(p(V), Gs)),
                    sequent(Left, Right))
       ->
       u'14'1(reduce'ii'in(sequent(nil(), Gs),
                           sequent(Left, cons(p(V), Right))))
     , u'14'1(reduce'ii'out()) -> reduce'ii'out()
     , reduce'ii'in(sequent(nil(), nil()), sequent(F1, F2)) ->
       u'15'1(intersect'ii'in(F1, F2))
     , u'15'1(intersect'ii'out()) -> reduce'ii'out()
     , tautology'i'in(F) ->
       u'16'1(reduce'ii'in(sequent(nil(), cons(F, nil())),
                           sequent(nil(), nil())))
     , u'16'1(reduce'ii'out()) -> tautology'i'out()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..