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


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


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given RelTRS could be proven:

(0) RelTRS
(1) RelTRSRRRProof [EQUIVALENT, 60 ms]
(2) RelTRS
(3) RelTRSRRRProof [EQUIVALENT, 10 ms]
(4) RelTRS
(5) RelTRSRRRProof [EQUIVALENT, 6 ms]
(6) RelTRS
(7) RIsEmptyProof [EQUIVALENT, 0 ms]
(8) YES


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

(0)
Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:

   topB(i, N1, y) -> topA(1, T1, y)
   topA(i, x, N2) -> topB(0, x, T2)
   topB(i, S1, y) -> topA(i, N1, y)
   topA(i, x, S2) -> topB(i, x, N2)
   topA(i, N1, T2) -> topB(i, N1, S2)
   topA(1, T1, T2) -> topB(1, T1, S2)

The relative TRS consists of the following S rules:

   topA(i, N1, y) -> topA(1, T1, y)
   topB(i, x, N2) -> topB(0, x, T2)
   topA(i, S1, y) -> topA(i, N1, y)
   topB(i, x, S2) -> topB(i, x, N2)
   topB(i, N1, T2) -> topB(i, N1, S2)
   topB(1, T1, T2) -> topB(1, T1, S2)


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

(1) RelTRSRRRProof (EQUIVALENT)
We used the following monotonic ordering for rule removal:
Polynomial interpretation [POLO]:

   POL(0) = 0
   POL(1) = 0
   POL(N1) = 1
   POL(N2) = 0
   POL(S1) = 1
   POL(S2) = 0
   POL(T1) = 0
   POL(T2) = 0
   POL(topA(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(topB(x_1, x_2, x_3)) = x_1 + x_2 + x_3
With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
Rules from R:

   topB(i, N1, y) -> topA(1, T1, y)
Rules from S:

   topA(i, N1, y) -> topA(1, T1, y)




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

(2)
Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:

   topA(i, x, N2) -> topB(0, x, T2)
   topB(i, S1, y) -> topA(i, N1, y)
   topA(i, x, S2) -> topB(i, x, N2)
   topA(i, N1, T2) -> topB(i, N1, S2)
   topA(1, T1, T2) -> topB(1, T1, S2)

The relative TRS consists of the following S rules:

   topB(i, x, N2) -> topB(0, x, T2)
   topA(i, S1, y) -> topA(i, N1, y)
   topB(i, x, S2) -> topB(i, x, N2)
   topB(i, N1, T2) -> topB(i, N1, S2)
   topB(1, T1, T2) -> topB(1, T1, S2)


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

(3) RelTRSRRRProof (EQUIVALENT)
We used the following monotonic ordering for rule removal:
Polynomial interpretation [POLO]:

   POL(0) = 0
   POL(1) = 0
   POL(N1) = 0
   POL(N2) = 0
   POL(S1) = 1
   POL(S2) = 0
   POL(T1) = 0
   POL(T2) = 0
   POL(topA(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(topB(x_1, x_2, x_3)) = x_1 + x_2 + x_3
With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
Rules from R:

   topB(i, S1, y) -> topA(i, N1, y)
Rules from S:

   topA(i, S1, y) -> topA(i, N1, y)




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

(4)
Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:

   topA(i, x, N2) -> topB(0, x, T2)
   topA(i, x, S2) -> topB(i, x, N2)
   topA(i, N1, T2) -> topB(i, N1, S2)
   topA(1, T1, T2) -> topB(1, T1, S2)

The relative TRS consists of the following S rules:

   topB(i, x, N2) -> topB(0, x, T2)
   topB(i, x, S2) -> topB(i, x, N2)
   topB(i, N1, T2) -> topB(i, N1, S2)
   topB(1, T1, T2) -> topB(1, T1, S2)


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

(5) RelTRSRRRProof (EQUIVALENT)
We used the following monotonic ordering for rule removal:
Polynomial interpretation [POLO]:

   POL(0) = 0
   POL(1) = 0
   POL(N1) = 0
   POL(N2) = 0
   POL(S2) = 0
   POL(T1) = 0
   POL(T2) = 0
   POL(topA(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(topB(x_1, x_2, x_3)) = x_1 + x_2 + x_3
With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
Rules from R:

   topA(i, x, N2) -> topB(0, x, T2)
   topA(i, x, S2) -> topB(i, x, N2)
   topA(i, N1, T2) -> topB(i, N1, S2)
   topA(1, T1, T2) -> topB(1, T1, S2)
Rules from S:
none




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

(6)
Obligation:
Relative term rewrite system:
R is empty.
The relative TRS consists of the following S rules:

   topB(i, x, N2) -> topB(0, x, T2)
   topB(i, x, S2) -> topB(i, x, N2)
   topB(i, N1, T2) -> topB(i, N1, S2)
   topB(1, T1, T2) -> topB(1, T1, S2)


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

(7) RIsEmptyProof (EQUIVALENT)
The TRS R is empty. Hence, termination is trivially proven.
----------------------------------------

(8)
YES