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


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


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given RelTRS could be proven:

(0) RelTRS
(1) RelTRSRRRProof [EQUIVALENT, 28 ms]
(2) RelTRS
(3) RIsEmptyProof [EQUIVALENT, 0 ms]
(4) YES


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

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

   f(x, 0) -> s(x)
   g(x) -> h(x, gen)
   h(0, x) -> f(x, x)
   a -> b

The relative TRS consists of the following S rules:

   gen -> s(gen)


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

(1) RelTRSRRRProof (EQUIVALENT)
We used the following monotonic ordering for rule removal:
f/2(YES,YES)
0/0)
s/1)YES(
g/1(YES)
h/2(YES,YES)
gen/0)
a/0)
b/0)

Quasi precedence:
0 > f_2 > gen
g_1 > h_2 > f_2 > gen
a > b > gen


Status:
f_2: [2,1]
0: multiset status
g_1: [1]
h_2: [2,1]
gen: multiset status
a: multiset status
b: multiset status

With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
Rules from R:

   f(x, 0) -> s(x)
   g(x) -> h(x, gen)
   h(0, x) -> f(x, x)
   a -> b
Rules from S:
none




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

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

   gen -> s(gen)


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

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

(4)
YES