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TRS Stand 20472 pair #381715790
details
property
value
status
complete
benchmark
PEANO_nokinds_noand_iGM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n027.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
3.46778297424 seconds
cpu usage
3.448640211
max memory
4.7120384E7
stage attributes
key
value
output-size
82657
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. 0 : [] --> o U11 : [o * o] --> o U12 : [o] --> o U21 : [o] --> o U31 : [o * o] --> o U41 : [o * o * o] --> o U42 : [o * o * o] --> o active : [o] --> o isNat : [o] --> o mark : [o] --> o plus : [o * o] --> o s : [o] --> o tt : [] --> o active(U11(tt, X)) => mark(U12(isNat(X))) active(U12(tt)) => mark(tt) active(U21(tt)) => mark(tt) active(U31(tt, X)) => mark(X) active(U41(tt, X, Y)) => mark(U42(isNat(Y), X, Y)) active(U42(tt, X, Y)) => mark(s(plus(Y, X))) active(isNat(0)) => mark(tt) active(isNat(plus(X, Y))) => mark(U11(isNat(X), Y)) active(isNat(s(X))) => mark(U21(isNat(X))) active(plus(X, 0)) => mark(U31(isNat(X), X)) active(plus(X, s(Y))) => mark(U41(isNat(Y), Y, X)) mark(U11(X, Y)) => active(U11(mark(X), Y)) mark(tt) => active(tt) mark(U12(X)) => active(U12(mark(X))) mark(isNat(X)) => active(isNat(X)) mark(U21(X)) => active(U21(mark(X))) mark(U31(X, Y)) => active(U31(mark(X), Y)) mark(U41(X, Y, Z)) => active(U41(mark(X), Y, Z)) mark(U42(X, Y, Z)) => active(U42(mark(X), Y, Z)) mark(s(X)) => active(s(mark(X))) mark(plus(X, Y)) => active(plus(mark(X), mark(Y))) mark(0) => active(0) U11(mark(X), Y) => U11(X, Y) U11(X, mark(Y)) => U11(X, Y) U11(active(X), Y) => U11(X, Y) U11(X, active(Y)) => U11(X, Y) U12(mark(X)) => U12(X) U12(active(X)) => U12(X) isNat(mark(X)) => isNat(X) isNat(active(X)) => isNat(X) U21(mark(X)) => U21(X) U21(active(X)) => U21(X) U31(mark(X), Y) => U31(X, Y) U31(X, mark(Y)) => U31(X, Y) U31(active(X), Y) => U31(X, Y) U31(X, active(Y)) => U31(X, Y) U41(mark(X), Y, Z) => U41(X, Y, Z) U41(X, mark(Y), Z) => U41(X, Y, Z) U41(X, Y, mark(Z)) => U41(X, Y, Z) U41(active(X), Y, Z) => U41(X, Y, Z) U41(X, active(Y), Z) => U41(X, Y, Z) U41(X, Y, active(Z)) => U41(X, Y, Z) U42(mark(X), Y, Z) => U42(X, Y, Z) U42(X, mark(Y), Z) => U42(X, Y, Z) U42(X, Y, mark(Z)) => U42(X, Y, Z) U42(active(X), Y, Z) => U42(X, Y, Z) U42(X, active(Y), Z) => U42(X, Y, Z) U42(X, Y, active(Z)) => U42(X, Y, Z) s(mark(X)) => s(X) s(active(X)) => s(X) plus(mark(X), Y) => plus(X, Y) plus(X, mark(Y)) => plus(X, Y) plus(active(X), Y) => plus(X, Y) plus(X, active(Y)) => plus(X, Y) 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#(U11(tt, X)) =#> mark#(U12(isNat(X))) 1] active#(U11(tt, X)) =#> U12#(isNat(X)) 2] active#(U11(tt, X)) =#> isNat#(X) 3] active#(U12(tt)) =#> mark#(tt) 4] active#(U21(tt)) =#> mark#(tt) 5] active#(U31(tt, X)) =#> mark#(X) 6] active#(U41(tt, X, Y)) =#> mark#(U42(isNat(Y), X, Y)) 7] active#(U41(tt, X, Y)) =#> U42#(isNat(Y), X, Y) 8] active#(U41(tt, X, Y)) =#> isNat#(Y) 9] active#(U42(tt, X, Y)) =#> mark#(s(plus(Y, X))) 10] active#(U42(tt, X, Y)) =#> s#(plus(Y, X)) 11] active#(U42(tt, X, Y)) =#> plus#(Y, X) 12] active#(isNat(0)) =#> mark#(tt) 13] active#(isNat(plus(X, Y))) =#> mark#(U11(isNat(X), Y))
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