SRS Relative pair #487082017

details

property	value
status	complete
benchmark	zr02.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	Mixed_relative_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.47887 seconds
cpu usage	6.79758
user time	6.43118
system time	0.366401
max virtual memory	5.6403676E7
max residence set size	884628.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given RelTRS could be proven:

(0) RelTRS
(1) RelTRSRRRProof [EQUIVALENT, 63 ms]
(2) RelTRS
(3) RelTRSRRRProof [EQUIVALENT, 9 ms]
(4) RelTRS
(5) RelTRSRRRProof [EQUIVALENT, 100 ms]
(6) RelTRS
(7) RIsEmptyProof [EQUIVALENT, 0 ms]
(8) YES


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

   n(s(x1)) -> s(x1)
   o(s(x1)) -> s(x1)
   n(o(p(x1))) -> o(n(x1))

The relative TRS consists of the following S rules:

   t(x1) -> t(c(n(x1)))
   p(s(x1)) -> s(x1)
   o(n(x1)) -> n(o(x1))
   p(n(x1)) -> m(p(x1))
   p(m(x1)) -> m(p(x1))
   o(m(x1)) -> n(o(x1))
   n(p(x1)) -> p(n(x1))
   c(p(x1)) -> p(c(x1))
   c(m(x1)) -> m(c(x1))
   c(n(x1)) -> n(c(x1))
   c(o(x1)) -> o(c(x1))
   c(o(x1)) -> o(x1)


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

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

   POL(c(x_1)) = x_1
   POL(m(x_1)) = x_1
   POL(n(x_1)) = x_1
   POL(o(x_1)) = 1 + x_1
   POL(p(x_1)) = x_1
   POL(s(x_1)) = x_1
   POL(t(x_1)) = x_1
With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
Rules from R:

   o(s(x1)) -> s(x1)
Rules from S:
none




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

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

   n(s(x1)) -> s(x1)
   n(o(p(x1))) -> o(n(x1))

The relative TRS consists of the following S rules:

   t(x1) -> t(c(n(x1)))
   p(s(x1)) -> s(x1)
   o(n(x1)) -> n(o(x1))
   p(n(x1)) -> m(p(x1))
   p(m(x1)) -> m(p(x1))
   o(m(x1)) -> n(o(x1))
   n(p(x1)) -> p(n(x1))
   c(p(x1)) -> p(c(x1))
   c(m(x1)) -> m(c(x1))
   c(n(x1)) -> n(c(x1))
   c(o(x1)) -> o(c(x1))
   c(o(x1)) -> o(x1)


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

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

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