/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

(0) QTRS
(1) QTRSRRRProof [EQUIVALENT, 35 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, 0) -> x
   +(x, s(y)) -> s(+(x, y))
   +(0, s(y)) -> s(y)
   s(+(0, y)) -> s(y)

Q is empty.

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

(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Knuth-Bendix order [KBO] with precedence:+_2 > s_1 > 0

and weight map:

   0=1
   s_1=1
   +_2=0

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, 0) -> x
   +(x, s(y)) -> s(+(x, y))
   +(0, s(y)) -> s(y)
   s(+(0, y)) -> s(y)




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

(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