TRS Conditional pair #516978577

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	n035.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.70194983482 seconds
cpu usage	7.301202078
max memory	5.12794624E8

stage attributes

key	value
output-size	10336
starexec-result	MAYBE

output

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


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MAYBE
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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, 8 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].
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(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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