/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

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: merge(nil(),nil(),X) -> X
    2: merge(nil(),cons(Y,U),V) -> merge(U,nil(),cons(Y,V))
    3: merge(cons(W,P),X1,Y1) -> merge(X1,P,cons(W,Y1))
    4: _(X1,X2) -> X1
    5: _(X1,X2) -> X2
Number of strict rules: 5
Direct POLO(bPol) ... removes: 4 1 3 5 2
      merge	w: 2 * x1 + 2 * x2 + x3 + 2282
      _ 	w: 2 * x1 + 2 * x2 + 1
      nil	w: 1
      cons	w: x1 + x2 + 610
Number of strict rules: 0

...
Input TRS:
    1: merge(nil(),nil(),X) -> X
    2: merge(nil(),cons(Y,U),V) -> merge(U,nil(),cons(Y,V))
    3: merge(cons(W,P),X1,Y1) -> merge(X1,P,cons(W,Y1))
    4: _(X1,X2) -> X1
    5: _(X1,X2) -> X2
Number of strict rules: 5
Direct POLO(bPol) ... removes: 4 1 3 5 2
      merge	w: 2 * x1 + 2 * x2 + x3 + 2282
      _ 	w: 2 * x1 + 2 * x2 + 1
      nil	w: 1
      cons	w: x1 + x2 + 610
Number of strict rules: 0
>>YES

******** Signature ********
 map : ((nat -> nat),list) -> list
 nil : list
 cons : (nat,list) -> list
******** Computation rules ********
 (4)  map(G1,nil) => nil
 (5)  map(H1,cons(W1,P1)) => cons(H1[W1],map(H1,P1))


******** General Schema criterion ********
Found constructors: cons, nil
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (1) merge(nil,nil,X) => X
 (meta X)[is acc in nil,nil,X] [is positive in nil] [is positive in nil] [is acc in X]  >>True
Checking  (2) merge(nil,cons(Y,U),V) => merge(U,nil,cons(Y,V))
 (fun merge=merge) subterm comparison of args w. LR LR >>False

Try again using status RL
Checking  (1) merge(nil,nil,X) => X
 (meta X)[is acc in nil,nil,X] [is positive in nil] [is positive in nil] [is acc in X]  >>True
Checking  (2) merge(nil,cons(Y,U),V) => merge(U,nil,cons(Y,V))
 (fun merge=merge) subterm comparison of args w. RL RL >>False

Try again using status Mul
Checking  (1) merge(nil,nil,X) => X
 (meta X)[is acc in nil,nil,X] [is positive in nil] [is positive in nil] [is acc in X]  >>True
Checking  (2) merge(nil,cons(Y,U),V) => merge(U,nil,cons(Y,V))
 (fun merge=merge) subterm comparison of args w. Mul Mul >>False
Found constructors: nil, cons
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (4) map(G1,nil) => nil
 (fun map>nil) >>True
Checking  (5) map(H1,cons(W1,P1)) => cons(H1[W1],map(H1,P1))
 (fun map>cons)
 (meta H1)[is acc in H1,cons(W1,P1)] [is acc in H1] 
 (meta W1)[is acc in H1,cons(W1,P1)] [is positive in cons(W1,P1)] [is acc in W1] 
 (fun map=map) subterm comparison of args w. LR LR
 (meta H1)[is acc in H1,cons(W1,P1)] [is acc in H1] 
 (meta P1)[is acc in H1,cons(W1,P1)] [is positive in cons(W1,P1)] [is acc in P1]  >>True
#SN!
******** Signature ********
 cons : (nat,list) -> list
 map : ((nat -> nat),list) -> list
 merge : (list,list,list) -> list
 nil : list
******** Computation Rules ********
 (1)  merge(nil,nil,X) => X
 (2)  merge(nil,cons(Y,U),V) => merge(U,nil,cons(Y,V))
 (3)  merge(cons(W,P),X1,Y1) => merge(X1,P,cons(W,Y1))
 (4)  map(G1,nil) => nil
 (5)  map(H1,cons(W1,P1)) => cons(H1[W1],map(H1,P1))

YES