TRS Stand 20472 pair #381709794

details

property	value
status	complete
benchmark	worm_wrong.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n087.star.cs.uiowa.edu
space	Hydras

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	26.3603010178 seconds
cpu usage	65.112864752
max memory	4.986720256E9

stage attributes

key	value
output-size	18512
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 0 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 1 ms]
        (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) UsableRulesProof [EQUIVALENT, 0 ms]
        (12) QDP
        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) YES
    (15) QDP
        (16) UsableRulesProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QDP
        (21) TransformationProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QDPOrderProof [EQUIVALENT, 189 ms]
        (24) QDP
        (25) QDPOrderProof [EQUIVALENT, 105 ms]
        (26) QDP
        (27) QDPOrderProof [EQUIVALENT, 25 ms]
        (28) QDP
        (29) QDPOrderProof [EQUIVALENT, 2404 ms]
        (30) QDP
        (31) PisEmptyProof [EQUIVALENT, 0 ms]
        (32) YES


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

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

   .(.(x, y), z) -> .(x, .(y, z))
   a(f(x)) -> f(a(x))
   a(.(x, y)) -> .(a(x), y)
   a(b1(x)) -> b1(a(x))
   f(b(x)) -> b(f(x))
   .(b(x), y) -> b(.(x, y))
   b1(b(x)) -> b(b(x))
   a(f(.(0, x))) -> b1(.(f(.(0, x)), .(0, f(x))))
   a(f(0)) -> b1(.(f(0), 0))
   f(.(0, x)) -> b(.(0, f(x)))
   f(0) -> b(0)
   c(b(x)) -> c(a(x))
   a(b(x)) -> b(a(x))

Q is empty.

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

(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   .^1(.(x, y), z) -> .^1(x, .(y, z))
   .^1(.(x, y), z) -> .^1(y, z)
   A(f(x)) -> F(a(x))
   A(f(x)) -> A(x)
   A(.(x, y)) -> .^1(a(x), y)
   A(.(x, y)) -> A(x)
   A(b1(x)) -> B1(a(x))
   A(b1(x)) -> A(x)
   F(b(x)) -> F(x)
   .^1(b(x), y) -> .^1(x, y)
   A(f(.(0, x))) -> B1(.(f(.(0, x)), .(0, f(x))))
   A(f(.(0, x))) -> .^1(f(.(0, x)), .(0, f(x)))
   A(f(.(0, x))) -> .^1(0, f(x))
   A(f(.(0, x))) -> F(x)
   A(f(0)) -> B1(.(f(0), 0))
   A(f(0)) -> .^1(f(0), 0)
   F(.(0, x)) -> .^1(0, f(x))
   F(.(0, x)) -> F(x)

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