/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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 w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRSRRRProof [EQUIVALENT, 85 ms]
(2) QTRS
(3) RisEmptyProof [EQUIVALENT, 0 ms]
(4) YES


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

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

   *(x, *(y, z)) -> *(otimes(x, y), z)
   *(1, y) -> y
   *(+(x, y), z) -> oplus(*(x, z), *(y, z))
   *(x, oplus(y, z)) -> oplus(*(x, y), *(x, z))

Q is empty.

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

(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Quasi precedence:
*_2 > otimes_2
*_2 > oplus_2
+_2 > oplus_2


Status:
*_2: [2,1]
otimes_2: multiset status
1: multiset status
+_2: [1,2]
oplus_2: [2,1]

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

   *(x, *(y, z)) -> *(otimes(x, y), z)
   *(1, y) -> y
   *(+(x, y), z) -> oplus(*(x, z), *(y, z))
   *(x, oplus(y, z)) -> oplus(*(x, y), *(x, z))




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

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

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

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

(4)
YES