TRS Condi 20667 pair #381732992

details

property	value
status	complete
benchmark	361.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n112.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.02812004089 seconds
cpu usage	4.876783955
max memory	3.2741376E8

stage attributes

key	value
output-size	10347
starexec-result	MAYBE

output

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


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Quasi decreasingness of the given CTRS could not be shown:

(0) CTRS
(1) CTRSToQTRSProof [SOUND, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 0 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) UsableRulesProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (16) YES
    (17) QDP
        (18) UsableRulesProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (21) YES
    (22) QDP
        (23) NonTerminationLoopProof [COMPLETE, 0 ms]
        (24) NO


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

   m(x, 0) -> x
   m(0, y) -> 0
   m(s(x), s(y)) -> m(x, y)
   greater(s(x), s(y)) -> greater(x, y)
   greater(s(x), 0) -> true
   leq(s(x), s(y)) -> leq(x, y)
   leq(0, x) -> true

The conditional TRS C consists of the following conditional rules:

   div(x, y) -> pair(0, y) <= greater(y, x) -> true
   div(x, y) -> pair(s(q), r) <= leq(y, x) -> true, div(m(x, y), y) -> pair(q, r)


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(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:

   div(x, y) -> U1(greater(y, x), y)
   U1(true, y) -> pair(0, y)
   div(x, y) -> U2(leq(y, x), x, y)
   U2(true, x, y) -> U3(div(m(x, y), y))
   U3(pair(q, r)) -> pair(s(q), r)
   m(x, 0) -> x
   m(0, y) -> 0
   m(s(x), s(y)) -> m(x, y)
   greater(s(x), s(y)) -> greater(x, y)
   greater(s(x), 0) -> true
   leq(s(x), s(y)) -> leq(x, y)
   leq(0, x) -> true

Q is empty.

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(3) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
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(4)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   DIV(x, y) -> U1^1(greater(y, x), y)
   DIV(x, y) -> GREATER(y, x)

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