TRS Equational pair #487523160

details

property	value
status	complete
benchmark	AC04.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n184.star.cs.uiowa.edu
space	AProVE_AC_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.59628295898 seconds
cpu usage	6.16085392
max memory	3.01432832E8

stage attributes

key	value
output-size	28143
starexec-result	YES

output

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


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given ETRS could be proven:

(0) ETRS
(1) EquationalDependencyPairsProof [EQUIVALENT, 56 ms]
(2) EDP
(3) EDependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) EDP
        (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (7) EDP
        (8) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (9) EDP
        (10) PisEmptyProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) EDP
        (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (14) EDP
        (15) EDPPoloProof [EQUIVALENT, 0 ms]
        (16) EDP
        (17) PisEmptyProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) EDP
        (20) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (21) EDP
        (22) EUsableRulesReductionPairsProof [EQUIVALENT, 3 ms]
        (23) EDP
        (24) ERuleRemovalProof [EQUIVALENT, 0 ms]
        (25) EDP
        (26) EDPPoloProof [EQUIVALENT, 11 ms]
        (27) EDP
        (28) PisEmptyProof [EQUIVALENT, 0 ms]
        (29) YES
    (30) EDP
        (31) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (32) EDP
        (33) EDPPoloProof [EQUIVALENT, 0 ms]
        (34) EDP
        (35) EDPPoloProof [EQUIVALENT, 34 ms]
        (36) EDP
        (37) PisEmptyProof [EQUIVALENT, 0 ms]
        (38) YES


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

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

   plus(x, 0) -> x
   plus(x, s(y)) -> s(plus(x, y))
   times(x, 0) -> 0
   times(x, s(y)) -> plus(x, times(x, y))
   minus(x, 0) -> x
   minus(s(x), s(y)) -> minus(x, y)
   div(0, s(y)) -> 0
   div(s(x), s(y)) -> s(div(minus(x, y), s(y)))

The set E consists of the following equations:

   plus(x, y) == plus(y, x)
   times(x, y) == times(y, x)
   plus(plus(x, y), z) == plus(x, plus(y, z))
   times(times(x, y), z) == times(x, times(y, z))


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

(1) EquationalDependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,DA_STEIN] we result in the following initial EDP problem:
The TRS P consists of the following rules:

   PLUS(x, s(y)) -> PLUS(x, y)
   TIMES(x, s(y)) -> PLUS(x, times(x, y))
   TIMES(x, s(y)) -> TIMES(x, y)
   MINUS(s(x), s(y)) -> MINUS(x, y)
   DIV(s(x), s(y)) -> DIV(minus(x, y), s(y))
   DIV(s(x), s(y)) -> MINUS(x, y)
   PLUS(plus(x, s(y)), ext) -> PLUS(s(plus(x, y)), ext)
   PLUS(plus(x, s(y)), ext) -> PLUS(x, y)
   TIMES(times(x, 0), ext) -> TIMES(0, ext)
   TIMES(times(x, s(y)), ext) -> TIMES(plus(x, times(x, y)), ext)
   TIMES(times(x, s(y)), ext) -> PLUS(x, times(x, y))
   TIMES(times(x, s(y)), ext) -> TIMES(x, y)

The TRS R consists of the following rules:

   plus(x, 0) -> x

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