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TRS Stand 20472 pair #381716745
details
property
value
status
complete
benchmark
Ex3_3_25_Bor03_iGM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n033.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
1.1345307827 seconds
cpu usage
1.120307432
max memory
2.6554368E7
stage attributes
key
value
output-size
40777
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. active : [o] --> o app : [o * o] --> o cons : [o * o] --> o from : [o] --> o mark : [o] --> o nil : [] --> o prefix : [o] --> o s : [o] --> o zWadr : [o * o] --> o active(app(nil, X)) => mark(X) active(app(cons(X, Y), Z)) => mark(cons(X, app(Y, Z))) active(from(X)) => mark(cons(X, from(s(X)))) active(zWadr(nil, X)) => mark(nil) active(zWadr(X, nil)) => mark(nil) active(zWadr(cons(X, Y), cons(Z, U))) => mark(cons(app(Z, cons(X, nil)), zWadr(Y, U))) active(prefix(X)) => mark(cons(nil, zWadr(X, prefix(X)))) mark(app(X, Y)) => active(app(mark(X), mark(Y))) mark(nil) => active(nil) mark(cons(X, Y)) => active(cons(mark(X), Y)) mark(from(X)) => active(from(mark(X))) mark(s(X)) => active(s(mark(X))) mark(zWadr(X, Y)) => active(zWadr(mark(X), mark(Y))) mark(prefix(X)) => active(prefix(mark(X))) app(mark(X), Y) => app(X, Y) app(X, mark(Y)) => app(X, Y) app(active(X), Y) => app(X, Y) app(X, active(Y)) => app(X, Y) cons(mark(X), Y) => cons(X, Y) cons(X, mark(Y)) => cons(X, Y) cons(active(X), Y) => cons(X, Y) cons(X, active(Y)) => cons(X, Y) from(mark(X)) => from(X) from(active(X)) => from(X) s(mark(X)) => s(X) s(active(X)) => s(X) zWadr(mark(X), Y) => zWadr(X, Y) zWadr(X, mark(Y)) => zWadr(X, Y) zWadr(active(X), Y) => zWadr(X, Y) zWadr(X, active(Y)) => zWadr(X, Y) prefix(mark(X)) => prefix(X) prefix(active(X)) => prefix(X) We use the dependency pair framework as described in [Kop12, Ch. 6/7], with static dependency pairs (see [KusIsoSakBla09] and the adaptation for AFSMs in [Kop12, Ch. 7.8]). We thus obtain the following dependency pair problem (P_0, R_0, minimal, formative): Dependency Pairs P_0: 0] active#(app(nil, X)) =#> mark#(X) 1] active#(app(cons(X, Y), Z)) =#> mark#(cons(X, app(Y, Z))) 2] active#(app(cons(X, Y), Z)) =#> cons#(X, app(Y, Z)) 3] active#(app(cons(X, Y), Z)) =#> app#(Y, Z) 4] active#(from(X)) =#> mark#(cons(X, from(s(X)))) 5] active#(from(X)) =#> cons#(X, from(s(X))) 6] active#(from(X)) =#> from#(s(X)) 7] active#(from(X)) =#> s#(X) 8] active#(zWadr(nil, X)) =#> mark#(nil) 9] active#(zWadr(X, nil)) =#> mark#(nil) 10] active#(zWadr(cons(X, Y), cons(Z, U))) =#> mark#(cons(app(Z, cons(X, nil)), zWadr(Y, U))) 11] active#(zWadr(cons(X, Y), cons(Z, U))) =#> cons#(app(Z, cons(X, nil)), zWadr(Y, U)) 12] active#(zWadr(cons(X, Y), cons(Z, U))) =#> app#(Z, cons(X, nil)) 13] active#(zWadr(cons(X, Y), cons(Z, U))) =#> cons#(X, nil) 14] active#(zWadr(cons(X, Y), cons(Z, U))) =#> zWadr#(Y, U) 15] active#(prefix(X)) =#> mark#(cons(nil, zWadr(X, prefix(X)))) 16] active#(prefix(X)) =#> cons#(nil, zWadr(X, prefix(X))) 17] active#(prefix(X)) =#> zWadr#(X, prefix(X)) 18] active#(prefix(X)) =#> prefix#(X) 19] mark#(app(X, Y)) =#> active#(app(mark(X), mark(Y))) 20] mark#(app(X, Y)) =#> app#(mark(X), mark(Y)) 21] mark#(app(X, Y)) =#> mark#(X) 22] mark#(app(X, Y)) =#> mark#(Y) 23] mark#(nil) =#> active#(nil) 24] mark#(cons(X, Y)) =#> active#(cons(mark(X), Y)) 25] mark#(cons(X, Y)) =#> cons#(mark(X), Y) 26] mark#(cons(X, Y)) =#> mark#(X) 27] mark#(from(X)) =#> active#(from(mark(X))) 28] mark#(from(X)) =#> from#(mark(X)) 29] mark#(from(X)) =#> mark#(X) 30] mark#(s(X)) =#> active#(s(mark(X))) 31] mark#(s(X)) =#> s#(mark(X)) 32] mark#(s(X)) =#> mark#(X) 33] mark#(zWadr(X, Y)) =#> active#(zWadr(mark(X), mark(Y))) 34] mark#(zWadr(X, Y)) =#> zWadr#(mark(X), mark(Y)) 35] mark#(zWadr(X, Y)) =#> mark#(X) 36] mark#(zWadr(X, Y)) =#> mark#(Y) 37] mark#(prefix(X)) =#> active#(prefix(mark(X))) 38] mark#(prefix(X)) =#> prefix#(mark(X)) 39] mark#(prefix(X)) =#> mark#(X)
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