/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Quasi decreasingness of the given CTRS could be proven:

(0) CTRS
(1) CTRSToQTRSProof [SOUND, 0 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 0 ms]
(4) QTRS
(5) RisEmptyProof [EQUIVALENT, 0 ms]
(6) YES


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

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

   s(a) -> t
   s(b) -> t
   a -> c
   b -> c
   g(x, x) -> h(x, x)

The conditional TRS C consists of the following conditional rules:

   f(x) -> A <= s(x) -> t
   f(x) -> B <= s(x) -> t


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

(1) CTRSToQTRSProof (SOUND)
The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC].
----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   f(x) -> U1(s(x))
   U1(t) -> A
   U1(t) -> B
   s(a) -> t
   s(b) -> t
   a -> c
   b -> c
   g(x, x) -> h(x, x)

Q is empty.

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

(3) QTRSRRRProof (EQUIVALENT)
Used ordering:
Knuth-Bendix order [KBO] with precedence:f_1 > U1_1 > s_1 > g_2 > t > h_2 > b > a > c > B > A

and weight map:

   t=2
   A=3
   B=3
   a=1
   b=1
   c=1
   f_1=2
   U1_1=1
   s_1=1
   g_2=0
   h_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:

   f(x) -> U1(s(x))
   U1(t) -> A
   U1(t) -> B
   s(a) -> t
   s(b) -> t
   a -> c
   b -> c
   g(x, x) -> h(x, x)




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

(4)
Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.

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

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

(6)
YES