TRS Equational pair #487092881

details

property	value
status	complete
benchmark	AC46.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	Mixed_C

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.54677 seconds
cpu usage	6.29461
user time	6.03198
system time	0.262631
max virtual memory	1.8343376E7
max residence set size	345700.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 ETRS could be proven:

(0) ETRS
(1) EquationalDependencyPairsProof [EQUIVALENT, 0 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) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (16) EDP
        (17) PisEmptyProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) EDP
        (20) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (21) EDP
        (22) EDPPoloProof [EQUIVALENT, 0 ms]
        (23) EDP
        (24) PisEmptyProof [EQUIVALENT, 0 ms]
        (25) YES
    (26) EDP
        (27) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (28) EDP
        (29) PisEmptyProof [EQUIVALENT, 0 ms]
        (30) YES
    (31) EDP
        (32) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (33) EDP
        (34) EDPPoloProof [EQUIVALENT, 0 ms]
        (35) EDP
        (36) PisEmptyProof [EQUIVALENT, 0 ms]
        (37) YES
    (38) EDP
        (39) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (40) EDP
        (41) EDPPoloProof [EQUIVALENT, 0 ms]
        (42) EDP
        (43) EDPPoloProof [EQUIVALENT, 22 ms]
        (44) EDP
        (45) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (46) TRUE


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

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

   eq(0, 0) -> true
   eq(0, s(x)) -> false
   eq(s(x), 0) -> false
   eq(s(x), s(y)) -> eq(x, y)
   le(0, y) -> true
   le(s(x), 0) -> false
   le(s(x), s(y)) -> le(x, y)
   app(nil, y) -> y
   app(add(n, x), y) -> add(n, app(x, y))
   min(add(n, nil)) -> n
   min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x)))
   if_min(true, add(n, add(m, x))) -> min(add(n, x))
   if_min(false, add(n, add(m, x))) -> min(add(m, x))
   rm(n, nil) -> nil
   rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x))
   if_rm(true, n, add(m, x)) -> rm(n, x)
   if_rm(false, n, add(m, x)) -> add(m, rm(n, x))
   minsort(nil, nil) -> nil
   minsort(add(n, x), y) -> if_minsort(eq(n, min(add(n, x))), add(n, x), y)
   if_minsort(true, add(n, x), y) -> add(n, minsort(app(rm(n, x), y), nil))
   if_minsort(false, add(n, x), y) -> minsort(x, add(n, y))

The set E consists of the following equations:

   eq(x, y) == eq(y, x)


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

(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:

   EQ(s(x), s(y)) -> EQ(x, y)
   LE(s(x), s(y)) -> LE(x, y)
   APP(add(n, x), y) -> APP(x, y)
   MIN(add(n, add(m, x))) -> IF_MIN(le(n, m), add(n, add(m, x)))

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actions all output return to TRS Equational