TRS Standard pair #615297961

details

property	value
status	complete
benchmark	3.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n135.star.cs.uiowa.edu
space	Secret_07_TRS

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	24.0966579914 seconds
cpu usage	58.400448876
max memory	2.853871616E9

stage attributes

key	value
output-size	29687
starexec-result	"YES"

output

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


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished


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, 0 ms]
        (7) QDP
        (8) TransformationProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) DependencyGraphProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) TransformationProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) DependencyGraphProof [EQUIVALENT, 0 ms]
        (15) QDP
        (16) TransformationProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) DependencyGraphProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) TransformationProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) DependencyGraphProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) UsableRulesProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) TransformationProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) DependencyGraphProof [EQUIVALENT, 0 ms]
        (29) TRUE
    (30) QDP
        (31) UsableRulesProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) QDPOrderProof [EQUIVALENT, 79 ms]
        (34) QDP
        (35) QDPOrderProof [EQUIVALENT, 26 ms]
        (36) QDP
        (37) TransformationProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) QDPOrderProof [EQUIVALENT, 89 ms]
        (40) QDP
        (41) QDPOrderProof [EQUIVALENT, 96 ms]
        (42) QDP
        (43) QDPOrderProof [EQUIVALENT, 866 ms]
        (44) QDP
        (45) PisEmptyProof [EQUIVALENT, 0 ms]
        (46) YES
    (47) QDP
        (48) UsableRulesProof [EQUIVALENT, 0 ms]
        (49) QDP
        (50) QDPOrderProof [EQUIVALENT, 0 ms]
        (51) QDP
        (52) UsableRulesProof [EQUIVALENT, 0 ms]
        (53) QDP
        (54) MRRProof [EQUIVALENT, 0 ms]
        (55) QDP
        (56) PisEmptyProof [EQUIVALENT, 0 ms]
        (57) YES


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

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

   i(x, x) -> i(a, b)
   g(x, x) -> g(a, b)
   h(s(f(x))) -> h(f(x))
   f(s(x)) -> s(s(f(h(s(x)))))
   f(g(s(x), y)) -> f(g(x, s(y)))
   h(g(x, s(y))) -> h(g(s(x), y))
   h(i(x, y)) -> i(i(c, h(h(y))), x)
   g(a, g(x, g(b, g(a, g(x, y))))) -> g(a, g(a, g(a, g(x, g(b, g(b, y))))))

Q is empty.

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

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

(2)
Obligation:
Q DP problem:

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS Standard