/export/starexec/sandbox2/solver/bin/starexec_run_hrs /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


MAYBE

We split firstr-order part and higher-order part, and do modular checking by a general modularity.

******** FO SN check ********
Check SN using NaTT (Nagoya Termination Tool)
Input TRS:
    1: plusc(X1,0()) -> X1
    2: plusc(Y1,s(U1)) -> s(plusc(Y1,U1))
    3: _(X1,X2) -> X1
    4: _(X1,X2) -> X2
Number of strict rules: 4
Direct POLO(bPol) ... removes: 4 1 3 2
      s 	w: x1 + 8856
      _ 	w: 2 * x1 + x2 + 1
      0 	w: 1
      plusc	w: 2 * x1 + 2 * x2 + 1237
Number of strict rules: 0

...
Input TRS:
    1: plusc(X1,0()) -> X1
    2: plusc(Y1,s(U1)) -> s(plusc(Y1,U1))
    3: _(X1,X2) -> X1
    4: _(X1,X2) -> X2
Number of strict rules: 4
Direct POLO(bPol) ... removes: 4 1 3 2
      s 	w: x1 + 8856
      _ 	w: 2 * x1 + x2 + 1
      0 	w: 1
      plusc	w: 2 * x1 + 2 * x2 + 1237
Number of strict rules: 0
>>YES

******** Signature ********
 foldl : (((nat,nat) -> nat),nat,list) -> nat
 yap : ((nat -> nat),nat) -> nat
 xap : (((nat,nat) -> nat),nat,nat) -> nat
 nil : list
 cons : (nat,list) -> list
 sum : list -> nat
 plusc : (nat,nat) -> nat
 0 : nat
******** Computation rules ********
 (1)  foldl(%X.%Y.yap(xap(F,%X),%Y),Y,nil) => Y
 (2)  foldl(%Z.%U.yap(xap(G,%Z),%U),V,cons(W,P)) => foldl(%V.%W.yap(xap(G,%V),%W),yap(xap(G,V),W),P)
 (5)  sum(V1) => foldl(%F.%G.yap(xap(plusc,%F),%G),0,V1)
 (6)  xap(I1,P1) => I1[P1]
 (7)  yap(F2,Y2) => F2[Y2]


******** General Schema criterion ********
Found constructors: 0, cons, nil, s
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (1) foldl(%X.%Y.yap(xap(F,%X),%Y),Y,nil) => Y
 (meta Y)[is acc in %X.%Y.yap(xap(F,%X),%Y),Y,nil] [is positive in yap(xap(F,%X),%Y)] [is acc in Y]  >>True
Checking  (2) foldl(%Z.%U.yap(xap(G,%Z),%U),V,cons(W,P)) => foldl(%V.%W.yap(xap(G,%V),%W),yap(xap(G,V),W),P)
 (fun foldl=foldl) subterm comparison of args w. LR LR >>False

Try again using status RL
Checking  (1) foldl(%X.%Y.yap(xap(F,%X),%Y),Y,nil) => Y
 (meta Y)[is acc in %X.%Y.yap(xap(F,%X),%Y),Y,nil] [is positive in yap(xap(F,%X),%Y)] [is acc in Y]  >>True
Checking  (2) foldl(%Z.%U.yap(xap(G,%Z),%U),V,cons(W,P)) => foldl(%V.%W.yap(xap(G,%V),%W),yap(xap(G,V),W),P)
 (fun foldl=foldl) subterm comparison of args w. RL RL
 (fun foldl>yap)
 (fun foldl>xap)
 (meta G)[is acc in %Z.%U.yap(xap(G,%Z),%U),V,cons(W,P)] [is positive in yap(xap(G,%Z),%U)] [is positive in cons(W,P)]  >>False

Try again using status Mul
Checking  (1) foldl(%X.%Y.yap(xap(F,%X),%Y),Y,nil) => Y
 (meta Y)[is acc in %X.%Y.yap(xap(F,%X),%Y),Y,nil] [is positive in yap(xap(F,%X),%Y)] [is acc in Y]  >>True
Checking  (2) foldl(%Z.%U.yap(xap(G,%Z),%U),V,cons(W,P)) => foldl(%V.%W.yap(xap(G,%V),%W),yap(xap(G,V),W),P)
 (fun foldl=foldl) subterm comparison of args w. Mul Mul >>False
Found constructors: nil, cons, plusc, 0
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (1) foldl(%X.%Y.yap(xap(F,%X),%Y),Y,nil) => Y
 (meta Y)[is acc in %X.%Y.yap(xap(F,%X),%Y),Y,nil] [is positive in yap(xap(F,%X),%Y)] [is acc in Y]  >>True
Checking  (2) foldl(%Z.%U.yap(xap(G,%Z),%U),V,cons(W,P)) => foldl(%V.%W.yap(xap(G,%V),%W),yap(xap(G,V),W),P)
 (fun foldl=foldl) subterm comparison of args w. LR LR >>False

Try again using status RL
Checking  (1) foldl(%X.%Y.yap(xap(F,%X),%Y),Y,nil) => Y
 (meta Y)[is acc in %X.%Y.yap(xap(F,%X),%Y),Y,nil] [is positive in yap(xap(F,%X),%Y)] [is acc in Y]  >>True
Checking  (2) foldl(%Z.%U.yap(xap(G,%Z),%U),V,cons(W,P)) => foldl(%V.%W.yap(xap(G,%V),%W),yap(xap(G,V),W),P)
 (fun foldl=foldl) subterm comparison of args w. RL RL
 (fun foldl>yap)
 (fun foldl>xap)
 (meta G)[is acc in %Z.%U.yap(xap(G,%Z),%U),V,cons(W,P)] [is positive in yap(xap(G,%Z),%U)] [is positive in cons(W,P)]  >>False

Try again using status Mul
Checking  (1) foldl(%X.%Y.yap(xap(F,%X),%Y),Y,nil) => Y
 (meta Y)[is acc in %X.%Y.yap(xap(F,%X),%Y),Y,nil] [is positive in yap(xap(F,%X),%Y)] [is acc in Y]  >>True
Checking  (2) foldl(%Z.%U.yap(xap(G,%Z),%U),V,cons(W,P)) => foldl(%V.%W.yap(xap(G,%V),%W),yap(xap(G,V),W),P)
 (fun foldl=foldl) subterm comparison of args w. Mul Mul >>False
#No idea..
******** Signature ********
 0 : nat
 cons : (nat,list) -> list
 foldl : (((nat,nat) -> nat),nat,list) -> nat
 nil : list
 plusc : (nat,nat) -> nat
 s : nat -> nat
 sum : list -> nat
 xap : (((nat,nat) -> nat),nat,nat) -> nat
 yap : ((nat -> nat),nat) -> nat
******** Computation Rules ********
 (1)  foldl(%X.%Y.yap(xap(F,%X),%Y),Y,nil) => Y
 (2)  foldl(%Z.%U.yap(xap(G,%Z),%U),V,cons(W,P)) => foldl(%V.%W.yap(xap(G,%V),%W),yap(xap(G,V),W),P)
 (3)  plusc(X1,0) => X1
 (4)  plusc(Y1,s(U1)) => s(plusc(Y1,U1))
 (5)  sum(V1) => foldl(%F.%G.yap(xap(plusc,%F),%G),0,V1)
 (6)  xap(I1,P1) => I1[P1]
 (7)  yap(F2,Y2) => F2[Y2]

MAYBE