SRS Relat 19260 pair #381725118

details

property	value
status	complete
benchmark	zr02new.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n077.star.cs.uiowa.edu
space	Mixed_relative_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.80641698837 seconds
cpu usage	8.206542288
max memory	1.171030016E9

stage attributes

key	value
output-size	5915
starexec-result	YES

output

/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 59 ms]
(2) RelTRS
(3) RelTRSRRRProof [EQUIVALENT, 14 ms]
(4) RelTRS
(5) RelTRSRRRProof [EQUIVALENT, 52 ms]
(6) RelTRS
(7) RelTRSRRRProof [EQUIVALENT, 42 ms]
(8) RelTRS
(9) RIsEmptyProof [EQUIVALENT, 1 ms]
(10) YES


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

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

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

The relative TRS consists of the following S rules:

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


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(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)) = x_1
   POL(p(x_1)) = 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:

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

The relative TRS consists of the following S rules:

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

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