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


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRSRRRProof [EQUIVALENT, 26 ms]
(2) QTRS
(3) RisEmptyProof [EQUIVALENT, 0 ms]
(4) YES


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(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   __(X, nil) -> X
   __(nil, X) -> X
   and(tt, X) -> activate(X)
   isList(V) -> isNeList(activate(V))
   isList(n__nil) -> tt
   isList(n____(V1, V2)) -> and(isList(activate(V1)), n__isList(activate(V2)))
   isNeList(V) -> isQid(activate(V))
   isNeList(n____(V1, V2)) -> and(isList(activate(V1)), n__isNeList(activate(V2)))
   isNeList(n____(V1, V2)) -> and(isNeList(activate(V1)), n__isList(activate(V2)))
   isNePal(V) -> isQid(activate(V))
   isNePal(n____(I, __(P, I))) -> and(isQid(activate(I)), n__isPal(activate(P)))
   isPal(V) -> isNePal(activate(V))
   isPal(n__nil) -> tt
   isQid(n__a) -> tt
   isQid(n__e) -> tt
   isQid(n__i) -> tt
   isQid(n__o) -> tt
   isQid(n__u) -> tt
   nil -> n__nil
   __(X1, X2) -> n____(X1, X2)
   isList(X) -> n__isList(X)
   isNeList(X) -> n__isNeList(X)
   isPal(X) -> n__isPal(X)
   a -> n__a
   e -> n__e
   i -> n__i
   o -> n__o
   u -> n__u
   activate(n__nil) -> nil
   activate(n____(X1, X2)) -> __(X1, X2)
   activate(n__isList(X)) -> isList(X)
   activate(n__isNeList(X)) -> isNeList(X)
   activate(n__isPal(X)) -> isPal(X)
   activate(n__a) -> a
   activate(n__e) -> e
   activate(n__i) -> i
   activate(n__o) -> o
   activate(n__u) -> u
   activate(X) -> X

Q is empty.

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(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Knuth-Bendix order [KBO] with precedence:u > activate_1 > o > i > isPal_1 > n__nil > e > n__o > n__isList_1 > a > n__u > n__i > n__e > n__a > n_____2 > nil > n__isPal_1 > n__isNeList_1 > isQid_1 > isNePal_1 > isNeList_1 > isList_1 > tt > and_2 > ___2

and weight map:

   nil=3
   tt=7
   n__nil=1
   n__a=6
   n__e=6
   n__i=6
   n__o=6
   n__u=6
   a=7
   e=7
   i=7
   o=8
   u=7
   activate_1=2
   isList_1=7
   isNeList_1=4
   n__isList_1=5
   isQid_1=1
   n__isNeList_1=2
   isNePal_1=4
   n__isPal_1=19
   isPal_1=20
   ___2=10
   and_2=0
   n_____2=9

The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   __(X, nil) -> X
   __(nil, X) -> X
   and(tt, X) -> activate(X)
   isList(V) -> isNeList(activate(V))
   isList(n__nil) -> tt
   isList(n____(V1, V2)) -> and(isList(activate(V1)), n__isList(activate(V2)))
   isNeList(V) -> isQid(activate(V))
   isNeList(n____(V1, V2)) -> and(isList(activate(V1)), n__isNeList(activate(V2)))
   isNeList(n____(V1, V2)) -> and(isNeList(activate(V1)), n__isList(activate(V2)))
   isNePal(V) -> isQid(activate(V))
   isNePal(n____(I, __(P, I))) -> and(isQid(activate(I)), n__isPal(activate(P)))
   isPal(V) -> isNePal(activate(V))
   isPal(n__nil) -> tt
   isQid(n__a) -> tt
   isQid(n__e) -> tt
   isQid(n__i) -> tt
   isQid(n__o) -> tt
   isQid(n__u) -> tt
   nil -> n__nil
   __(X1, X2) -> n____(X1, X2)
   isList(X) -> n__isList(X)
   isNeList(X) -> n__isNeList(X)
   isPal(X) -> n__isPal(X)
   a -> n__a
   e -> n__e
   i -> n__i
   o -> n__o
   u -> n__u
   activate(n__nil) -> nil
   activate(n____(X1, X2)) -> __(X1, X2)
   activate(n__isList(X)) -> isList(X)
   activate(n__isNeList(X)) -> isNeList(X)
   activate(n__isPal(X)) -> isPal(X)
   activate(n__a) -> a
   activate(n__e) -> e
   activate(n__i) -> i
   activate(n__o) -> o
   activate(n__u) -> u
   activate(X) -> X




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(2)
Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.

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(3) RisEmptyProof (EQUIVALENT)
The TRS R is empty. Hence, termination is trivially proven.
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(4)
YES